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 A151983 Numbers congruent to {0, 1} mod 32. 4
 0, 1, 32, 33, 64, 65, 96, 97, 128, 129, 160, 161, 192, 193, 224, 225, 256, 257, 288, 289, 320, 321, 352, 353, 384, 385, 416, 417, 448, 449, 480, 481, 512, 513, 544, 545, 576, 577, 608, 609, 640, 641, 672, 673, 704, 705, 736, 737, 768, 769, 800, 801, 832, 833, 864, 865 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Numbers n such that n^2 - n is divisible by 32. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA From Bruno Berselli, Jan 26 2011: (Start) G.f.: (1+31*x)*x^2/((1+x)*(1-x)^2). a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. a(n) = (32*n - 15*(-1)^n - 47)/2. Sum_{k=1..n} a(k) == 0 (mod A004526(n)) for n > 1. (End) a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(k)=2^(k+4) for k > 0. - Philippe Deléham, Oct 16 2011 MATHEMATICA Flatten[{#, #+1}&/@(32Range[0, 35])]  (* Harvey P. Dale, Mar 11 2011 *) CoefficientList[Series[(1 + 31 x) x / ((1 + x) (1 - x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *) PROG (PARI) a(n)=(32*n-15*(-1)^n-47)/2 \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A004526, A030308, A070454. Sequence in context: A054032 A134843 A134844 * A022402 A194768 A217845 Adjacent sequences:  A151980 A151981 A151982 * A151984 A151985 A151986 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Aug 23 2009 STATUS approved

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Last modified May 27 17:53 EDT 2020. Contains 334664 sequences. (Running on oeis4.)