OFFSET
2,2
COMMENTS
See the k=4 column of table A054772(n, k), with more explanations there.
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (6,-12,2,27,-36,0,36,-27,-2,12,-6,1).
FORMULA
From Colin Barker, Oct 09 2016: (Start)
G.f.: x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5+272*x^6+28*x^7+x^8) / ((1-x)^9*(1+x)^3).
a(n) = (n^8-6*n^6+14*n^4)/96 for n even.
a(n) = (n^8-6*n^6+14*n^4-6*n^2-3)/96 for n odd. (End)
From Stefan Hollos, Oct 16 2016: (Start)
a(n) = (C(n^2,4) + C(n^2/2,2) + n^2/2)/4 for n even,
a(n) = (C(n^2,4) + C((n^2-1)/2,2) + (n^2-1)/2)/4 for n odd. (End)
MATHEMATICA
CoefficientList[Series[x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5 +272*x^6+28*x^7+x^8)/((1-x)^9*(1+x)^3), {x, 0, 50}], x] (* G. C. Greubel, Oct 22 2018 *)
PROG
(PARI) Vec(x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5+272*x^6+28*x^7 +x^8)/((1-x)^9*(1+x)^3) + O(x^40)) \\ Colin Barker, Oct 16 2016
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5 +272*x^6+28*x^7+x^8)/((1-x)^9*(1+x)^3))); // G. C. Greubel, Oct 22 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 06 2016
STATUS
approved