3,2

Number of 3-dimensional cubes in n-dimensional hypercube - Henry Bottomley (se16(AT)btinternet.com), Apr 14 2000

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

With 3 leading zeros, binomial transform of C(n,3). - Paul Barry (pbarry(AT)wit.ie), Apr 10 2003

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

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

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

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]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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.

H. Izbicki, Ueber Unterbaeume eines Baumes, Monatshefte f\"{u}r Mathematik, 74 (1970), 56-62.

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.

Milan Janjic, Two Enumerative Functions

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

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.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for sequences related to Chebyshev polynomials.

Eric Weisstein's World of Mathematics, Hypercube

a(n)=2*a(n-1)+A001788(n-1)

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

E.g.f. (x^3/3!)exp(2x) (with 3 leading zeros) - Paul Barry (pbarry(AT)wit.ie), Apr 10 2003

seq((n^3-n)*2^(n-3)/3, n=2..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2007

A001789:=1/(2*z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]

seq(binomial(n+3, 3)*2^n, n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2008

Table[Binomial[n, 3]*2^(n - 3), {n, 3, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 18 2006

(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]

Cf. A001787, A001788, A003472.

For n>0, a(n+3) = 2 * A082138(n) = 8 * A080930(n+1).

Sequence in context: A125198 A128639 A004405 this_sequence A074412 A113071 A006726

Adjacent sequences: A001786 A001787 A001788 this_sequence A001790 A001791 A001792

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 15 2000

More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 18 2006