OFFSET
0,2
COMMENTS
If Y_i (i=1,2,3,4,5,6) are 2-blocks of a (n+6)-set X then a(n-5) is the number of 11-subsets of X intersecting each Y_i (i=1,2,3,4,5,6). - Milan Janjic, Oct 28 2007
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Milan Janjic, Two Enumerative Functions
Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.
Ross McPhedran, Numerical Investigations of the Keiper-Li Criterion for the Riemann Hypothesis, arXiv:2311.06294 [math.NT], 2023. See p. 6.
Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).
FORMULA
G.f.: ((1+x)/(1-x))^6.
a(n) = 4*n*(2/15*n^4+4/3*n^2+23/15) for n > 0. - S. Bujnowski (slawb(AT)atr.bydgoszcz.pl), Nov 26 2002
n*a(n) = 12*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018
MAPLE
for n from 1 to 8 do eval(4*n*(2/15*n^4+4/3*n^2+23/15)) od;
MATHEMATICA
{1}~Join~Table[4 n (2/15 n^4 + 4/3 n^2 + 23/15), {n, 29}] (* or *)
CoefficientList[Series[((1 + x)/(1 - x))^6, {x, 0, 29}], x] (* Michael De Vlieger, Oct 04 2016 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 12, 72, 292, 912, 2364, 5336}, 30] (* Harvey P. Dale, Jul 01 2020 *)
PROG
(PARI) a(n)=if(n, 4*n*(2*n^4+20*n^2+23)/15, 1) \\ Charles R Greathouse IV, Oct 04 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved