A140156 a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^5 if n is even.

1, 33, 60, 1084, 1209, 8985, 9328, 42096, 42825, 142825, 144156, 392988, 395185, 933009, 936384, 1984960, 1989873, 3879441, 3886300, 7086300, 7095561, 12249193, 12261360, 20223984, 20239609, 32120985, 32140668, 49351036, 49375425

Offset: 1

Author

Artur Jasinski, May 12 2008

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6, -1,1).

Crossrefs

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

Programs

Magma

[(1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6): n in [1..50]]; // G. C. Greubel, Jul 05 2018

Mathematica

a = {}; r = 3; s = 5; 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)^3,a+(n+1)^5]}; Transpose[ NestList[ nxt,{1,1},30]][[2]] (* or *) LinearRecurrence[ {1,6,-6,-15, 15,20,-20,-15,15,6,-6,-1,1},{1,33,60,1084,1209,8985,9328, 42096, 42825, 142825,144156, 392988,395185},40] (* Harvey P. Dale, Aug 27 2013 *)
Table[(1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6), {n, 1, 50}] (* G. C. Greubel, Jul 05 2018 *)

PARI

for(n=1, 50, print1((1/48)*(9*(-1 +(-1)^n) + 4*(1 -12(-1)^n)*n^2 + 12*(1 -(-1)^n)*n^3 + (16 + 30*(-1)^n)*n^4 + 12*(1 +(-1)^n)*n^5 + 4*n^6), ", ")) \\ G. C. Greubel, Jul 05 2018

Formula

G.f.: -x*(1 + 32*x + 21*x^2 + 832*x^3 - 22*x^4 + 2112*x^5 - 22*x^6 + 832*x^7 + 21*x^8 + 32*x^9 + x^10)/((1+x)^6*(x-1)^7). - R. J. Mathar, Feb 22 2009