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A140143
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a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^5 if n is even.
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1
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1, 33, 34, 1058, 1059, 8835, 8836, 41604, 41605, 141605, 141606, 390438, 390439, 928263, 928264, 1976840, 1976841, 3866409, 3866410, 7066410, 7066411, 12220043, 12220044, 20182668, 20182669, 32064045, 32064046
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..27.
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FORMULA
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a(n)=a(n-1)+{[1-(-1)^n]/2}+{[1+(-1)^n]/2}*n^5, with a(1)=1 a(n)=(1/8)-(1/8)*(-1)^n-(5/8)*(-1)^n*n^2-(1/24)*n^2+(1/2)*n+(1/12)*n^6+(1/4)*(-1)^n*n^5+(1/4)*n^5+(5/8) *(-1)^n*n^4+(5/24)*n^4, with n>=1 - Paolo P. Lava, Jun 06 2008
a(n)=a(n-1)+6a(n-2)-6a(n-3)-15a(n-4)+15a(n-5)+20a(n-6)-20a(n-7)-15a(n-8)+15a(n-9)+6a(n-10)-6a(n-11)-a(n-12)+a(n-13). G.f.: x*(-1-32*x+5*x^2-832*x^3-10*x^4-2112*x^5+10*x^6-832*x^7-5*x^8-32*x^9+x^10 )/((1+x)^6*(x-1)^7). [From R. J. Mathar, Feb 22 2009]
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MATHEMATICA
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a = {}; r = 0; 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*)
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CROSSREFS
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Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
Sequence in context: A260678 A329658 A344139 * A041543 A144425 A180329
Adjacent sequences: A140140 A140141 A140142 * A140144 A140145 A140146
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski, May 12 2008, corrected May 17 2008
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STATUS
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approved
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