A047436 Numbers that are congruent to {5, 6} mod 8.

5, 6, 13, 14, 21, 22, 29, 30, 37, 38, 45, 46, 53, 54, 61, 62, 69, 70, 77, 78, 85, 86, 93, 94, 101, 102, 109, 110, 117, 118, 125, 126, 133, 134, 141, 142, 149, 150, 157, 158, 165, 166, 173, 174, 181, 182, 189, 190

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

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

Crossrefs

Union of A004770 and A017137.

Programs

Mathematica

Select[Range[200], MemberQ[{5, 6}, Mod[#, 8]] &] (* Amiram Eldar, Dec 19 2021 *)

Formula

From Vincenzo Librandi, Aug 06 2010: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3).

a(n) = 8*n - a(n-1) - 5, n > 1. (End)

G.f. x*(5+x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/16 + log(2)/8 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 19 2021