Search: id:A001789
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%I A001789 M4522 N1916
%S A001789 1,8,40,160,560,1792,5376,15360,42240,112640,292864,745472,1863680,
%T A001789 4587520,11141120,26738688,63504384,149422080,348651520,807403520,
%U A001789 1857028096,4244635648,9646899200,21810380800,49073356800,109924319232
%N A001789 Binomial(n,3)*2^(n-3).
%C A001789 Number of 3-dimensional cubes in n-dimensional hypercube - Henry Bottomley 
               (se16(AT)btinternet.com), Apr 14 2000
%C A001789 With three leading zeros, this is the second binomial transform of (0,
               0,0,1,0,0,0,0,..) - Paul Barry (pbarry(AT)wit.ie), Mar 07 2003
%C A001789 With 3 leading zeros, binomial transform of C(n,3). - Paul Barry (pbarry(AT)wit.ie), 
               Apr 10 2003
%C A001789 Let M=[1,0,i;0,1,0;i,0,1], i=sqrt(-1). Then 1/det(I-xM)=1/(1-2x)^4. - 
               Paul Barry (pbarry(AT)wit.ie), Apr 27 2005
%C A001789 If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for 
               n>2, a(n+1) is equal to the number of (n+3)-subsets of X intersecting 
               each X_i (i=1,2,...,n). - Milan R. Janjic (agnus(AT)blic.net), Jul 
               21 2007
%C A001789 With a different offset, number of n-permutations (n=4) of 3 objects: 
               u, v, w with repetition allowed, containing exactly three u's. Example: 
               a(1)=8 because we have: uuuv, uuvu, uvuu, vuuu, uuuw, uuwu, uwuu 
               and wuuu - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 
               2008
%C A001789 With offset 0, a(n) is the number of ways to seperate [n] into four non-overlapping 
               intervals (allowed to be empty) and then choose a subset from each 
               interval. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443), Feb 
               07 2009]
%D A001789 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001789 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001789 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A001789 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 796.
%D A001789 H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 
               74 (1970), 56-62.
%D A001789 Jones, C. W.; Miller, J. C. P.; Conn, J. F. C.; Pankhurst, R. C.; Tables 
               of Chebyshev polynomials. Proc. Roy. Soc. Edinburgh. Sect. A. 62, 
               (1946). 187-203.
%H A001789 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A001789 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A001789 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001789 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A001789 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%H A001789 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Hypercube.html">Hypercube</a>
%F A001789 a(n)=2*a(n-1)+A001788(n-1)
%F A001789 G.f. (with three leading zeros): x^3/(1-2x)^4. With three leading zeros, 
               a(n)=8a(n-1)-24a(n-2)+32a(n-3)-16a(n-4), a(0)=a(1)=a(2)=0, a(3)=1. 
               - Paul Barry (pbarry(AT)wit.ie), Mar 07 2003
%F A001789 E.g.f. (x^3/3!)exp(2x) (with 3 leading zeros) - Paul Barry (pbarry(AT)wit.ie), 
               Apr 10 2003
%p A001789 seq((n^3-n)*2^(n-3)/3,n=2..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 25 2007
%p A001789 A001789:=1/(2*z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
%p A001789 seq(binomial(n+3,3)*2^n,n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jun 03 2008
%t A001789 Table[Binomial[n, 3]*2^(n - 3), {n, 3, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 18 2006
%o A001789 (Other) SAGE: [lucas_number1(n, 2, 0)*binomial(n,3)/4 for n in xrange(3, 
               29)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 
               2009]
%Y A001789 Cf. A001787, A001788, A003472.
%Y A001789 For n>0, a(n+3) = 2 * A082138(n) = 8 * A080930(n+1).
%Y A001789 Sequence in context: A125198 A128639 A004405 this_sequence A074412 A113071 
               A006726
%Y A001789 Adjacent sequences: A001786 A001787 A001788 this_sequence A001790 A001791 
               A001792
%K A001789 nonn,easy,nice
%O A001789 3,2
%A A001789 N. J. A. Sloane (njas(AT)research.att.com).
%E A001789 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000
%E A001789 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 18 2006

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