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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A047398, A047463.

Programs

Magma

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

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 *)

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