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 A212668 a(n) = (16/3)*(n+1)*n*(n-1) + 8*n^2 + 1. 6
 9, 65, 201, 449, 841, 1409, 2185, 3201, 4489, 6081, 8009, 10305, 13001, 16129, 19721, 23809, 28425, 33601, 39369, 45761, 52809, 60545, 69001, 78209, 88201, 99009, 110665, 123201, 136649, 151041, 166409, 182785, 200201, 218689, 238281, 259009, 280905, 304001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the difference between numbers of nonnegative multiples of 2*n+1 with even and odd digit sum in base 2*n in interval [0, 32*n^5). LINKS Colin Barker, Table of n, a(n) for n = 1..1000 V. Shevelev, On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m, arXiv:0710.3177 [math.NT], 2007. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^5(Pi*i/(2*n+1)) * sin(2*Pi*i/(2*n+1)). G.f.: x*(9+29*x-5*x^2-x^3) / (1-x)^4. - Colin Barker, Nov 30 2015 MATHEMATICA LinearRecurrence[{4, -6, 4, -1}, {9, 65, 201, 449}, 40] (* Vincenzo Librandi, Dec 01 2015 *) CoefficientList[Series[x (9+29x-5x^2-x^3)/(1-x)^4, {x, 0, 40}], x] (* Harvey P. Dale, Mar 29 2023 *) PROG (PARI) a(n)=16*(n+1)*n*(n-1)/3+8*n^2+1 \\ Charles R Greathouse IV, Oct 07 2015 (PARI) Vec(x*(9+29*x-5*x^2-x^3)/(1-x)^4 + O(x^100)) \\ Colin Barker, Nov 30 2015 (Magma) [(16/3)*(n+1)*n*(n-1)+8*n^2+1: n in [1..40]]; // Vincenzo Librandi, Dec 01 2015 CROSSREFS Cf. A038754, A084990, A091042, A212500, A212592. Sequence in context: A076287 A339997 A226929 * A020299 A250415 A237040 Adjacent sequences: A212665 A212666 A212667 * A212669 A212670 A212671 KEYWORD nonn,easy AUTHOR Vladimir Shevelev and Peter J. C. Moses, May 23 2012 STATUS approved

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Last modified December 6 16:13 EST 2023. Contains 367612 sequences. (Running on oeis4.)