A231307 Recurrence a(n) = a(n-2) + n^M for M=8, starting with a(0)=0, a(1)=1.

0, 1, 256, 6562, 65792, 397187, 1745408, 6161988, 18522624, 49208709, 118522624, 263567590, 548504320, 1079298311, 2024293376, 3642188936, 6319260672, 10617946377, 17339221248, 27601509418, 42939221248, 65424368779, 97815094784, 143735354060

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = Sum_{k=0..floor(n/2)} (n-2k)^8.

a(n) = 1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192). - Vaclav Kotesovec, Feb 14 2014

G.f.: x*(1+246*x+4047*x^2+11572*x^3+4047*x^4+246*x^5+x^6) / (1-x)^10.

Example

a(5) = 5^8 + 3^8 + 1^8 = 397187.

Mathematica

Table[1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192), {n, 0, 20}] (* Vaclav Kotesovec, Feb 14 2014 *)

Prog

(PARI) nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^8); print(a);
(PARI) concat(0, Vec(x*(1+246*x+4047*x^2+11572*x^3+4047*x^4+246*x^5+x^6)/(1-x)^10 + O(x^50))) \\ Colin Barker, Dec 22 2015
(Magma) [1/90*n*(n+1)*(n+2)*(5*n^6+30*n^5+20*n^4-120*n^3-16*n^2+288*n-192): n in [0..30]]; // Vincenzo Librandi, Dec 23 2015

Crossrefs

Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231306 (M=7), A231308 (M=9), A231309 (M=10).

Sequence in context: A179645 A056585 A321818 * A206129 A236214 A232959

Adjacent sequences: A231304 A231305 A231306 * A231308 A231309 A231310

Keyword

nonn,easy

Author

Stanislav Sykora, Nov 07 2013

Status

approved