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

1,3

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).

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)

Mathematica

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

Prog

(Magma) [n : n in [0..600] | n mod 19 in [0, 1]]; // Vincenzo Librandi, Feb 04 2020
(PARI) a(n) = (1/4)*(38*n - 55 - 17*(-1)^n); \\ David Lovler, Jul 25 2022

Crossrefs

Sequence in context: A274340 A241849 A054304 * A022109 A041730 A041732

Adjacent sequences: A151976 A151977 A151978 * A151980 A151981 A151982

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 23 2009

Status

approved