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 (8,-28,56,-70,56,-28,8,-1).
FORMULA
a(n) = Sum_{k=0..floor(n/2)}(n-2k)^6.
From Colin Barker, Dec 22 2015: (Start)
a(n) = 1/42*n*(3*n^6+21*n^5+42*n^4-56*n^2+32).
G.f.: x*(1+56*x+246*x^2+56*x^3+x^4) / (1-x)^8.
(End)
EXAMPLE
a(5) = 5^6 + 3^6 + 1^6 = 16355.
MAPLE
map(op, ListTools:-PartialSums([seq([(2*i)^6, (2*i+1)^6], i=0..50)])); # Robert Israel, Dec 22 2015
MATHEMATICA
Table[SeriesCoefficient[x (1 + 56 x + 246 x^2 + 56 x^3 + x^4)/(1 - x)^8, {x, 0, n}], {n, 0, 28}] (* Michael De Vlieger, Dec 22 2015 *)
PROG
(PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^6); print(a);
(PARI) concat(0, Vec(x*(1+56*x+246*x^2+56*x^3+x^4)/(1-x)^8 + O(x^50))) \\ Colin Barker, Dec 22 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, Nov 07 2013
STATUS
approved