A047353 Numbers that are congruent to {1, 2} mod 7.

1, 2, 8, 9, 15, 16, 22, 23, 29, 30, 36, 37, 43, 44, 50, 51, 57, 58, 64, 65, 71, 72, 78, 79, 85, 86, 92, 93, 99, 100, 106, 107, 113, 114, 120, 121, 127, 128, 134, 135, 141, 142, 148, 149, 155, 156, 162, 163, 169, 170

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• David Lovler, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Mathematica

LinearRecurrence[{1,1,-1},{1,2,8},50] (* Harvey P. Dale, Nov 29 2014 *)

PARI

a(n) = (14*n - 15 - 5*(-1)^n)/4 \\ David Lovler, Sep 11 2022

Formula

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

a(n) = 7*n/2 - 15/4 - 5*(-1)^n/4.

G.f.: x*(1 + x + 5*x^2) / ( (1+x)*(x-1)^2 ). (End)

E.g.f.: 5 + ((14*x -15)*exp(x) - 5*exp(-x))/4. - David Lovler, Sep 11 2022