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A140161 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^5 if n is even. 2
1, 33, 114, 1138, 1763, 9539, 11940, 44708, 51269, 151269, 165910, 414742, 443303, 981127, 1031752, 2080328, 2163849, 4053417, 4183738, 7383738, 7578219, 12731851, 13011692, 20974316, 21364941, 33246317, 33777758, 50988126 (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^4 + ((1 + (-1)^n)/2)*n^5, with a(1)=1.

a(n) = -1/8 + (1/4)*(-1)^n*n + (1/8)*(-1)^n - (1/2)*(-1)^n*n^3 + (1/6)*n^3 - (5/8)*(-1)^n*n^2 - (1/24)*n^2 - (1/60)*n + (1/12)*n^6 + (1/4)*(-1)^n*n^5 + (7/20)*n^5 + (3/8)*(-1)^n*n^4 + (11/24)*n^4, with n >= 1. (End)

G.f.: x*(-1 - 32*x - 75*x^2 - 832*x^3 - 154*x^4 - 2112*x^5 + 154*x^6 - 832*x^7 + 75*x^8 - 32*x^9 + x^10)/((1+x)^6*(x-1)^7). - R. J. Mathar, Feb 22 2009

MATHEMATICA

a = {}; r = 4; 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 *)

next[{a_, b_}]:={a+1, If[OddQ[a+1], b+(a+1)^4, b+(a+1)^5]}; Transpose[ NestList[ next[#]&, {1, 1}, 30]][[2]] (* Harvey P. Dale, Nov 23 2011 *)

Table[(1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*n^6), {n, 1, 50}] (* G. C. Greubel, Jul 05 2018 *)

PROG

(PARI) for(n=1, 50, print1((1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*n^6), ", ")) \\ G. C. Greubel, Jul 05 2018

(MAGMA) [(1/120)*(15*(-1 +(-1)^n) - 2*(1 -15*(-1)^n)*n - 5*(1 +15*(-1)^n)*n^2 + 20*(1 -3*(-1)^n)*n^3 + (55 + 45*(-1)^n)*n^4 + (42 +30*(-1)^n)*n^5 + 10*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: A198291 A044284 A044665 * A177211 A337626 A301633

Adjacent sequences:  A140158 A140159 A140160 * A140162 A140163 A140164

KEYWORD

nonn

AUTHOR

Artur Jasinski, May 12 2008

STATUS

approved

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Last modified November 30 06:28 EST 2021. Contains 349419 sequences. (Running on oeis4.)