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