A047417 Numbers that are congruent to {2, 3, 4, 6} mod 8.

2, 3, 4, 6, 10, 11, 12, 14, 18, 19, 20, 22, 26, 27, 28, 30, 34, 35, 36, 38, 42, 43, 44, 46, 50, 51, 52, 54, 58, 59, 60, 62, 66, 67, 68, 70, 74, 75, 76, 78, 82, 83, 84, 86, 90, 91, 92, 94, 98, 99, 100, 102, 106, 107, 108, 110, 114, 115, 116, 118, 122, 123

Offset

1,1

Links

Table of n, a(n) for n=1..62.

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

Formula

G.f.: x*(2+x+x^2+2*x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 25 2016: (Start)

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

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

a(2k) = A047398(k), a(2k-1) = A047463(k). (End)

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

Sum_{n>=1} (-1)^(n+1)/a(n) = (3-sqrt(2))*Pi/16 - (sqrt(2)+4)*log(2)/16 + sqrt(2)*log(sqrt(2)+2)/8. - Amiram Eldar, Dec 25 2021

Maple

A047417:=n->(8*n-5-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047417(n), n=1..100); # Wesley Ivan Hurt, May 25 2016

Mathematica

Flatten[#+{2, 3, 4, 6}&/@(8Range[0, 20])] (* Harvey P. Dale, Dec 20 2012 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 3, 4, 6]]; // Wesley Ivan Hurt, May 25 2016

Crossrefs

Cf. A047398, A047463.

Sequence in context: A353562 A347733 A347798 * A066936 A067027 A275108

Adjacent sequences: A047414 A047415 A047416 * A047418 A047419 A047420

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved