A151979 Numbers congruent to {0, 1} (mod 19).

0, 1, 19, 20, 38, 39, 57, 58, 76, 77, 95, 96, 114, 115, 133, 134, 152, 153, 171, 172, 190, 191, 209, 210, 228, 229, 247, 248, 266, 267, 285, 286, 304, 305, 323, 324, 342, 343, 361, 362, 380, 381, 399, 400, 418, 419, 437, 438, 456, 457, 475, 476, 494, 495, 513, 514, 532

Offset: 1

Author

N. J. A. Sloane, Aug 23 2009

Keywords

• nonn
• easy

Comments

Numbers m such that m^2 - m is divisible by 19.

Links

• David Lovler, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[n : n in [0..600] | n mod 19 in [0, 1]]; // Vincenzo Librandi, Feb 04 2020

Mathematica

Select[Range[0,600],MemberQ[{0,1},Mod[#,19]]&] (* Harvey P. Dale, Feb 11 2019 *)

PARI

a(n) = (1/4)*(38*n - 55 - 17*(-1)^n); \\ David Lovler, Jul 25 2022

Formula

a(n+1) = Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=1 and b(k)=19*2^(k-1) for k>0. - Philippe Deléham, Oct 19 2011

G.f.: x^2*(1+18*x)/((1-x)^2*(1+x)). - Colin Barker, Apr 09 2012

a(n) = a(n-1) + a(n-2) - a(n-3). - Colin Barker, Apr 09 2012

From Stefano Spezia, Feb 01 2020: (Start)

a(n) = (1/4)*(38*n - 55 - 17*(-1)^n).

E.g.f.: (19/2)*(x*(cosh(x) + sinh(x)) - sinh(x)) - 18*(cosh(x) - 1). (End)