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A135095 a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^2 if n is even. 2
1, 5, 248, 264, 3389, 3425, 20232, 20296, 79345, 79445, 240496, 240640, 611933, 612129, 1371504, 1371760, 2791617, 2791941, 5268040, 5268440, 9352541, 9353025, 15789368, 15789944, 25555569, 25556245, 39905152, 39905936, 60417085 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: -x*(x^8 - 4*x^7 + 236*x^6 + 12*x^5 + 1446*x^4 - 12*x^3 + 236*x^2 + 4*x + 1)*(x^2 + 1)/( (1+x)^6 * (x-1)^7 ). - R. J. Mathar, Feb 22 2009

a(n) = (1/24)*( 3 + 2*n + 5*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 2*n^6 - 3*(-1)^n*(1 - 2*n - 7*n^2 + 5*n^4 + 2*n^5) ), with n>=1. - Paolo P. Lava, Mar 02 2009

E.g.f.: (1/24)*( (-3 - 6*x - 17*x^2 + 240*x^3 - 75*x^4 + 6*x^5)*exp(x) + (3 + 24*x + 204*x^2 + 364*x^3 + 195*x^4 + 36*x^5 + 2*x^6)*exp(x) ). - G. C. Greubel, Sep 23 2016

MATHEMATICA

a = {}; r = 5; 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*)

Table[(1/24)*(3 + 2*n + 5*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 2*n^6 - 3*(-1)^n*(1 + n* (-2 - 7*n + 5*n^3 + 2*n^4))), {n, 1, 50}] (* G. C. Greubel, Sep 23 2016 *)

PROG

(PARI) for(n=1, 50, print1((1/24)*(3 + 2*n + 5*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 2*n^6 - 3*(-1)^n*(1 + n* (-2 - 7*n + 5*n^3 + 2*n^4))), ", ")) \\ G. C. Greubel, Jul 05 2018

(MAGMA) [(1/24)*(3 + 2*n + 5*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 2*n^6 - 3*(-1)^n*(1 + n* (-2 - 7*n + 5*n^3 + 2*n^4))): n in [1..50]]; // G. C. Greubel, Jul 05 2018

CROSSREFS

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

Sequence in context: A166943 A125533 A068727 * A219872 A282734 A115739

Adjacent sequences:  A135092 A135093 A135094 * A135096 A135097 A135098

KEYWORD

nonn

AUTHOR

Artur Jasinski, May 12 2008

STATUS

approved

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Last modified July 8 08:08 EDT 2020. Contains 335520 sequences. (Running on oeis4.)