OFFSET
0,3
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..9999
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
a(n) = Sum_{k=0..floor(n\2)} (n-2*k)^10.
From Colin Barker, Dec 22 2015: (Start)
a(n) = (1/66)*n*(3*n^10 + 33*n^9 + 110*n^8 - 528*n^6 + 2112*n^4 - 4224*n^2 + 2560).
G.f.: x*(1 + 1012*x + 46828*x^2 + 408364*x^3 + 901990*x^4 + 408364*x^5 + 46828*x^6 + 1012*x^7 + x^8) / (1-x)^12.
(End)
EXAMPLE
a(5) = 5^10 + 3^10 + 1^10 = 9824675.
MATHEMATICA
CoefficientList[Series[x (1 + 1012 x + 46828 x^2 + 408364 x^3 + 901990 x^4 + 408364 x^5 + 46828 x^6 + 1012 x^7 + x^8)/(1 - x)^12, {x, 0, 20}], x] (* Michael De Vlieger, Nov 20 2019 *)
PROG
(PARI) nmax=100; a=vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^10); print(a);
(PARI) concat(0, Vec(x*(1 +1012*x +46828*x^2 +408364*x^3 +901990*x^4 +408364*x^5 +46828*x^6 +1012*x^7 +x^8) / (1 -x)^12 + O(x^40))) \\ Colin Barker, Dec 22 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, Nov 07 2013
STATUS
approved