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A151979 Numbers congruent to {0, 1} (mod 19). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Numbers m such that m^2 - m is divisible by 19.
LINKS
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 23 2009
STATUS
approved

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Last modified May 27 17:52 EDT 2024. Contains 372880 sequences. (Running on oeis4.)