A231306 Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1.

0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825, 12393600, 25173996, 48225408, 87922513, 153638912, 258781888, 422074368, 669120561, 1034294400, 1562992300, 2314294400, 3364080841, 4808652288, 6768906288, 9395123712, 12872421913, 17426933888

Offset: 0

Author

Stanislav Sykora, Nov 07 2013

Keywords

• nonn
• easy

Examples

			a(5) = 5^7 + 3^7 + 1^7 = 80313.
		

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,-27,48,-42,0,42,-48,27,-8,1).

Crossrefs

Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231307 (M=8), A231308 (M=9), A231309 (M=10).

Programs

Mathematica

Table[SeriesCoefficient[x (1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/((1 - x)^9 (1 + x)), {x, 0, n}], {n, 0, 26}] (* Michael De Vlieger, Dec 22 2015 *)
LinearRecurrence[{8, -27, 48, -42, 0, 42, -48, 27, -8, 1}, {0, 1, 128, 2188, 16512, 80313, 296448, 903856, 2393600, 5686825}, 30] (* Vincenzo Librandi, Dec 23 2015 *)
nxt[{n_,a_,b_}]:={n+1,b,a+(n+1)^7}; NestList[nxt,{1,0,1},30][[All,2]] (* Harvey P. Dale, Jun 16 2022 *)

PARI

nmax=100; a = vector(nmax); a[2]=1; for(i=3, #a, a[i]=a[i-2]+(i-1)^7); print(a);

PARI

concat(0, Vec(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/((1-x)^9*(1+x)) + O(x^50))) \\ Colin Barker, Dec 22 2015

Formula

a(n) = Sum_{k=0..floor(n/2)} (n-2k)^7.

From Colin Barker, Dec 22 2015: (Start)

a(n) = 1/96*(6*n^8+48*n^7+112*n^6-224*n^4+256*n^2+51*((-1)^n-1)).

G.f.: x*(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6) / ((1-x)^9*(1+x)).

(End)