A047397 Numbers that are congruent to {0, 1, 2, 6} mod 8.

0, 1, 2, 6, 8, 9, 10, 14, 16, 17, 18, 22, 24, 25, 26, 30, 32, 33, 34, 38, 40, 41, 42, 46, 48, 49, 50, 54, 56, 57, 58, 62, 64, 65, 66, 70, 72, 73, 74, 78, 80, 81, 82, 86, 88, 89, 90, 94, 96, 97, 98, 102, 104, 105, 106, 110, 112, 113, 114, 118, 120, 121, 122

Offset

1,3

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*(1+x+4*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-11+i^(2*n)+(1+2*i)*i^(-n)+(1-2*i)*i^n)/4, where i=sqrt(-1).

a(2k) = A047452(k), a(2k-1) = A047467(k). (End)

E.g.f.: (4 + 2*sin(x) + cos(x) + (4*x - 6)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016

Sum_{n>=2} (-1)^n/a(n) = (sqrt(2)-1)*Pi/16 + log(2)/2 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 20 2021

Maple

A047397:=n->(8*n-11+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047397(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

Mathematica

Table[(8n-11+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 6, 8}, 70] (* Harvey P. Dale, Dec 31 2017 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 6]]; // Wesley Ivan Hurt, May 24 2016

Crossrefs

Cf. A047452, A047467.

Sequence in context: A342751 A120736 A130099 * A174331 A220116 A366059

Adjacent sequences: A047394 A047395 A047396 * A047398 A047399 A047400

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Wesley Ivan Hurt, May 24 2016

Status

approved