A140150 a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^4 if n is even.

1, 17, 26, 282, 307, 1603, 1652, 5748, 5829, 15829, 15950, 36686, 36855, 75271, 75496, 141032, 141321, 246297, 246658, 406658, 407099, 641355, 641884, 973660, 974285, 1431261, 1431990, 2046646, 2047487, 2857487, 2858448, 3907024, 3908113

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Index entries for linear recurrences with constant coefficients, signature (1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1).

Formula

G.f.: x*(1+16*x+4*x^2+176*x^3-10*x^4+176*x^5+4*x^6+16*x^7+x^8)/((1+x)^5*(x-1)^6). - R. J. Mathar, Feb 22 2009

a(n) = (6*n^5 + 15*n^4 + 20*n^3 + 15*n^2 + 4*n + (15*n^4 + 30*n^3 - 15*n^2 - 30*n)*(-1)^n)/60. - Charles R Greathouse IV, Jun 03 2026

Mathematica

a = {}; r = 2; s = 4; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a (*Artur Jasinski*)
nxt[{n_, a_}]:={n+1, If[EvenQ[n], a+(n+1)^2, a+(n+1)^4]}; NestList[nxt, {1, 1}, 40][[All, 2]] (* or *) LinearRecurrence[{1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {1, 17, 26, 282, 307, 1603, 1652, 5748, 5829, 15829, 15950}, 40] (* Harvey P. Dale, Aug 28 2017 *)

Prog

(PARI) a(n)=my(q=n\2); 16*q^5/5+8*q^4+20*q^3/3+[-13*q, 60*q^2+47*q+15][n%2+1]/15 \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.

Sequence in context: A171954 A336272 A154277 * A166658 A268330 A221282

Adjacent sequences: A140147 A140148 A140149 * A140151 A140152 A140153

Keyword

nonn,easy

Author

Artur Jasinski, May 12 2008

Status

approved