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 A140158 a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-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, with a(1)=1. a(n) = -1/8 + (1/2)*(-1)^n*n + (1/8)*(-1)^n - (1/2)*(-1)^n*n^3 + (1/6)*n^3 + (1/4)*n^2 + (7/30)*n + (1/10)*n^5 - (1/4)*(-1)^n*n^4 + (1/4)*n^4, with n >= 1. (End) 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 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113. Sequence in context: A111648 A013518 A166241 * A160875 A081542 A160877 Adjacent sequences:  A140155 A140156 A140157 * A140159 A140160 A140161 KEYWORD nonn AUTHOR Artur Jasinski, May 12 2008 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)