4,2

Number of 4D hypercubes in n-dimensional hypercube - Henry Bottomley (se16(AT)btinternet.com), Apr 14 2000.

With four leading zeros, binomial transform of C(n,4) - Paul Barry (pbarry(AT)wit.ie), Apr 10 2003

If X_1,X_2,...,X_n is a partition of a 2n-set X into 2-blocks then, for n>3, a(n) is equal to the number of (n+4)-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=5) of 3 objects: u, v, z, with repetition allowed, containing exactly four (4) u's. Example: a(1)=10 because we have uuuuv uuuvu uuvuu uvuuu vuuuu uuuuz uuuzu uuzuu uzuuu zuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008

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

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

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.

a(n)=2*a(n-1)+A001789(n-1)

G.f. 1/(1-2x)^5 E.g.f. exp(2x)(x^4/4!) (with 4 leading zeros) - Paul Barry (pbarry(AT)wit.ie), Apr 10 2003

A003472:=-1/(2*z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]

seq(binomial(n+4, 4)*2^n, n=0..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 12 2008

(Other) SAGE: [lucas_number2(n, 2, 0)*binomial(n, 4)/16for n in xrange(4, 28)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]

Cf. A001787, A001788, A001789.

Sequence in context: A144560 A076160 A004406 this_sequence A112502 A083585 A155633

Adjacent sequences: A003469 A003470 A003471 this_sequence A003473 A003474 A003475

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