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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 (1,6,-6,-15,15,20,-20,-15,15,6,-6, -1,1).

FORMULA

From Paolo P. Lava, Jun 06 2008: (Start)

a(n) = a(n-1) + ((1 - (-1)^n)/2)*n^3 + ((1 + (-1)^n)/2)*n^5, with a(1)=1.

a(n) = -3/16 + (3/16)*(-1)^n - (1/4)*(-1)^n*n^3 + (1/4)*n^3 - (-1)^n*n^2 + (1/12)*n^2 + (1/12)*n^6 + (1/4)*(-1)^n*n^5 + (1/4)*n^5 + (5/8)*(-1)^n*n^4 + (1/3)*n^4, with n >= 1. (End)

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

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 *)

PROG

(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

(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

CROSSREFS

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

Sequence in context: A043203 A043983 A080673 * A154600 A100593 A115160

Adjacent sequences:  A140153 A140154 A140155 * A140157 A140158 A140159

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, May 12 2008

STATUS

approved

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Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)