OFFSET
0,2
COMMENTS
If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-4) is the number of 9-subsets of X intersecting each Y_i (i=1,2,3,4,5). - Milan Janjic, Oct 28 2007
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Milan Janjic, Two Enumerative Functions
Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: ((1+x)/(1-x))^5.
a(n) = (4/3)*n^4 + (20/3)*n^2 + 2 for n > 0. - Michael De Vlieger, Oct 04 2016
n*a(n) = 10*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018
From Shel Kaphan, Mar 03 2023: (Start)
a(n) = 2*d*Hypergeometric2F1(1-d, 1-n, 2, 2) where d=5, for n>=1.
a(n) = A035599(n)*5/n, for n>0. (End)
MAPLE
4/3*n^4+20/3*n^2+2;
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 50, 170, 450, 1002}, 40] (* Harvey P. Dale, May 02 2016 *)
{1}~Join~Table[4/3 n^4 + 20/3 n^2 + 2, {n, 32}] (* or *)
CoefficientList[Series[((1 + x)/(1 - x))^5, {x, 0, 32}], x] (* Michael De Vlieger, Oct 04 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved