A047495 Numbers that are congruent to {2, 4, 5, 7} mod 8.

2, 4, 5, 7, 10, 12, 13, 15, 18, 20, 21, 23, 26, 28, 29, 31, 34, 36, 37, 39, 42, 44, 45, 47, 50, 52, 53, 55, 58, 60, 61, 63, 66, 68, 69, 71, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 93, 95, 98, 100, 101, 103, 106, 108, 109, 111, 114, 116, 117, 119, 122, 124

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Formula

G.f.: x*(2+x^2+x^3) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

From Wesley Ivan Hurt, May 27 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

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

a(2k) = A047535(k), a(2k-1) = A047617(k). (End)

E.g.f.: (2 + sin(x) - cos(x) + (4*x - 1)*exp(x))/2. - Ilya Gutkovskiy, May 27 2016

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

Maple

A047495:=n->(1+I)*(4*n-4*n*I+I-1+I^(1-n)-I^n)/4: seq(A047495(n), n=1..100); # Wesley Ivan Hurt, May 27 2016

Mathematica

Table[(1+I)*(4n-4n*I+I-1+I^(1-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 5, 7]]; // Wesley Ivan Hurt, May 27 2016

Crossrefs

Cf. A047535, A047617.

Sequence in context: A278490 A188029 A187951 * A005653 A188468 A364132

Adjacent sequences: A047492 A047493 A047494 * A047496 A047497 A047498

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved