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A140158
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a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even.
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2
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1, 3, 84, 88, 713, 719, 3120, 3128, 9689, 9699, 24340, 24352, 52913, 52927, 103552, 103568, 187089, 187107, 317428, 317448, 511929, 511951, 791792, 791816, 1182441, 1182467, 1713908, 1713936, 2421217, 2421247, 3344768, 3344800, 4530721
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
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FORMULA
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G.f.: x*(1 + 2*x + 76*x^2 - 6*x^3 + 230*x^4 + 6*x^5 + 76*x^6 - 2*x^7 + x^8)/((1+x)^5*(x-1)^6). - R. J. Mathar, Feb 22 2009
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MATHEMATICA
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a = {}; r = 4; s = 1; 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 *)
LinearRecurrence[{1, 5, -5, -10, 10, 10, -10, -5, 5, 1, -1}, {1, 3, 84, 88, 713, 719, 3120, 3128, 9689, 9699, 24340}, 50] (* or *) Table[(1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5), {n, 1, 50}] (* G. C. Greubel, Jul 05 2018 *)
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PROG
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(PARI) for(n=1, 50, print1((1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5), ", ")) \\ G. C. Greubel, Jul 05 2018
(Magma) [(1/120)*(15*(-1 +(-1)^n) + (28 + 60*(-1)^n)*n + 30*n^2 + 20*(1 - 3*(-1)^n)*n^3 + 30*(1 -(-1)^n)*n^4 + 12*n^5): n in [1..50]]; // G. C. Greubel, Jul 05 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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