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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
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6, -1,1).
FORMULA
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
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 12 2008
STATUS
approved