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

Author

N. J. A. Sloane, Aug 23 2009

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A004526, A030308, A070454.

Programs

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 *)

PARI

a(n)=(32*n-15*(-1)^n-47)/2 \\ Charles R Greathouse IV, Oct 16 2015

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