A047414 Numbers that are congruent to {0, 3, 4, 6} mod 8.

0, 3, 4, 6, 8, 11, 12, 14, 16, 19, 20, 22, 24, 27, 28, 30, 32, 35, 36, 38, 40, 43, 44, 46, 48, 51, 52, 54, 56, 59, 60, 62, 64, 67, 68, 70, 72, 75, 76, 78, 80, 83, 84, 86, 88, 91, 92, 94, 96, 99, 100, 102, 104, 107, 108, 110, 112, 115, 116, 118, 120, 123, 124

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^2*(3+x+2*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 24 2016: (Start)

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

a(n) = (8*n-7+i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).

a(2k) = A047398(k), a(2k-1) = A008586(k-1) for k>0. (End)

E.g.f.: (4 - cos(x) + 4*(x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016

Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16 - (2-sqrt(2))*Pi/16. - Amiram Eldar, Dec 21 2021

Maple

A047414:=n->(8*n-7+I^(2*n)-I^(-n)-I^n)/4: seq(A047414(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 3, 4, 6}, Mod[#, 8]]&] (* Harvey P. Dale, May 10 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4, 6]]; // Wesley Ivan Hurt, May 24 2016

Crossrefs

Cf. A008586, A047398.

Sequence in context: A325455 A337455 A080728 * A109402 A020901 A181714

Adjacent sequences: A047411 A047412 A047413 * A047415 A047416 A047417

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved