A231309 Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1.

0, 1, 1024, 59050, 1049600, 9824675, 61515776, 292299924, 1135257600, 3779084325, 11135257600, 29716508926, 73052621824, 167575000775, 362307276800, 744225391400, 1461818904576, 2760219291849, 5032286131200, 8891285549650, 15272286131200

Offset: 0

Author

Stanislav Sykora, Nov 07 2013

Keywords

• nonn
• easy

Examples

			a(5) = 5^10 + 3^10 + 1^10 = 9824675.
		

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).

Crossrefs

Cf. A001477 (M=1), A000292 (M=2), A105636 (M=3), A231303 (M=4), A231304 (M=5), A231305 (M=6), A231306 (M=7), A231307 (M=8), A231308 (M=9).

Programs

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 *)

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

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)