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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(a(k), k=1..n) == 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

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 January 17 14:12 EST 2019. Contains 319225 sequences. (Running on oeis4.)