A140157 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^0 if n is even.

1, 2, 83, 84, 709, 710, 3111, 3112, 9673, 9674, 24315, 24316, 52877, 52878, 103503, 103504, 187025, 187026, 317347, 317348, 511829, 511830, 791671, 791672, 1182297, 1182298, 1713739, 1713740, 2421021, 2421022, 3344543, 3344544, 4530465

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn

Links

• G. C. Greubel, 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).

Crossrefs

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

Programs

Magma

[(1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5): n in [1..50]]; // G. C. Greubel, Jul 05 2018

Mathematica

a = {}; r = 4; s = 0; 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 *)
LinearRecurrence[{1,5,-5,-10,10,10,-10,-5,5,1,-1}, {1, 2, 83, 84, 709, 710, 3111, 3112, 9673, 9674, 24315}, 50] (* or *) Table[(1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5), {n,1,50}] (* G. C. Greubel, Jul 05 2018 *)

PARI

for(n=1,50, print1((1/60)*(15*(-1 + (-1)^n) + (29 +15*(-1)^n)*n + 10*(1 -3*(-1)^n)*n^3 + 15*(1 -(-1)^n)*n^4 + 6*n^5), ", ")) \\ G. C. Greubel, Jul 05 2018

Formula

G.f.: x*(1 + x + 76*x^2 - 4*x^3 + 230*x^4 + 6*x^5 + 76*x^6 - 4*x^7 + x^8 + x^9)/((1+x)^5*(x-1)^6). - R. J. Mathar, Feb 22 2009