A140159 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^2 if n is even.

1, 5, 86, 102, 727, 763, 3164, 3228, 9789, 9889, 24530, 24674, 53235, 53431, 104056, 104312, 187833, 188157, 318478, 318878, 513359, 513843, 793684, 794260, 1184885, 1185561, 1717002, 1717786, 2425067, 2425967, 3349488, 3350512, 4536433

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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+4*x+76*x^2-4*x^3+230*x^4-4*x^5+76*x^6+4*x^7+x^8)/((1+x)^5*(x-1)^6). - R. J. Mathar, Feb 22 2009

Mathematica

a = {}; r = 4; s = 2; 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)^4, a+(n+1)^2]}; NestList[nxt, {1, 1}, 40][[All, 2]] (* Harvey P. Dale, Sep 21 2016 *)
LinearRecurrence[{1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {1, 5, 86, 102, 727, 763, 3164, 3228, 9789, 9889, 24530}, 50] (* or *) Table[(1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3), {n, 1, 50}] (* G. C. Greubel, Jul 05 2018 *)

Prog

(PARI) for(n=1, 50, print1((1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3), ", ")) \\ G. C. Greubel, Jul 05 2018
(Magma) [(1/60)*(n +n^2)* (4 + 30*(-1)^n + (11 -15*(-1)^n)*n + (9 -15*(-1)^n)*n^2 + 6*n^3): n in [1..50]]; // G. C. Greubel, Jul 05 2018

Crossrefs

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

Sequence in context: A309327 A363424 A174320 * A073862 A222983 A243075

Adjacent sequences: A140156 A140157 A140158 * A140160 A140161 A140162

Keyword

nonn

Author

Artur Jasinski, May 12 2008

Status

approved