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A151983
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Numbers congruent to {0, 1} mod 32.
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4
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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
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OFFSET
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1,3
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COMMENTS
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Numbers n such that n^2 - n is divisible by 32.
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LINKS
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FORMULA
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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)
E.g.f.: 31 + ((32*x - 47)*exp(x) - 15*exp(-x))/2. - David Lovler, Sep 10 2022
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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