A151983 Numbers congruent to {0, 1} mod 32.

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

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

E.g.f.: 31 + ((32*x - 47)*exp(x) - 15*exp(-x))/2. - David Lovler, Sep 10 2022

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