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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
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 (list; graph; refs; listen; history; text; internal format)
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

a(n)=a(n-1)+{[1-(-1)^n]/2}*n^2+{[1+(-1)^n]/2}*n^4, with a(1)=1 a(n)= -(1/2)*(-1)^n*n+(1/2)*(-1)^n*n^3+(1/3)*n^3-(1/4)*(-1)^n*n^2+(1/4)*n^2+(1/15)*n+(1/10)*n^5+(1/4) *(-1)^n*n^4+(1/4)*n^4, with n>=1 - Paolo P. Lava, Jun 06 2008

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). [From R. J. Mathar, Feb 22 2009]

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 *)

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

AUTHOR

Artur Jasinski, May 12 2008

STATUS

approved

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Last modified June 19 05:18 EDT 2021. Contains 345125 sequences. (Running on oeis4.)