A047274 Numbers that are congruent to {0, 1} mod 7.

0, 1, 7, 8, 14, 15, 21, 22, 28, 29, 35, 36, 42, 43, 49, 50, 56, 57, 63, 64, 70, 71, 77, 78, 84, 85, 91, 92, 98, 99, 105, 106, 112, 113, 119, 120, 126, 127, 133, 134, 140, 141, 147, 148, 154, 155, 161, 162, 168, 169

Offset

1,3

Comments

Nonnegative k such that k or 6*k + 1 is divisible by 7. - Bruno Berselli, Feb 13 2018

Links

David Lovler, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 7*n - a(n-1) - 13 for n>1, a(1)=0. - Vincenzo Librandi, Aug 05 2010

From R. J. Mathar, Oct 08 2011: (Start)

a(n) = 7*n/2 - 19/4 - 5*(-1)^n/4.

G.f.: x^2*(1 + 6*x) / ((1 + x)*(x - 1)^2). (End)

a(n+1) = Sum_{k>=0} A030308(n,k)*A135092(k). - Philippe Deléham, Oct 17 2011

E.g.f.: 6 + ((14*x - 19)*exp(x) - 5*exp(-x))/4. - David Lovler, Aug 31 2022

Prog

(PARI) forstep(n=0, 200, [1, 6], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Crossrefs

Cf. A030308, A135092.

Sequence in context: A286261 A136037 A085334 * A037368 A281710 A037970

Adjacent sequences: A047271 A047272 A047273 * A047275 A047276 A047277

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved