A047445 Numbers that are congruent to {1, 3, 5, 6} mod 8.

1, 3, 5, 6, 9, 11, 13, 14, 17, 19, 21, 22, 25, 27, 29, 30, 33, 35, 37, 38, 41, 43, 45, 46, 49, 51, 53, 54, 57, 59, 61, 62, 65, 67, 69, 70, 73, 75, 77, 78, 81, 83, 85, 86, 89, 91, 93, 94, 97, 99, 101, 102, 105, 107, 109, 110, 113, 115, 117, 118, 121, 123, 125

Offset

1,2

Links

Table of n, a(n) for n=1..63.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

G.f.: x*(1+2*x+2*x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, May 26 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-5-i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).

a(2k) = A047398(k), a(2k-1) = A016813(k-1) for k>0. (End)

E.g.f.: (4 - cos(x) + (4*x - 2)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = (4-sqrt(2))*Pi/16 + log(2)/8 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 24 2021

Maple

A047445:=n->(8*n-5-I^(2*n)-I^(-n)-I^n)/4: seq(A047445(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

Mathematica

Table[(8n-5-I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 5, 6]]; // Wesley Ivan Hurt, May 26 2016

Crossrefs

Cf. A016813, A047398.

Sequence in context: A367499 A324701 A047271 * A341349 A248638 A248881

Adjacent sequences: A047442 A047443 A047444 * A047446 A047447 A047448

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved