A047532 Numbers that are congruent to {0, 2, 3, 7} mod 8.

0, 2, 3, 7, 8, 10, 11, 15, 16, 18, 19, 23, 24, 26, 27, 31, 32, 34, 35, 39, 40, 42, 43, 47, 48, 50, 51, 55, 56, 58, 59, 63, 64, 66, 67, 71, 72, 74, 75, 79, 80, 82, 83, 87, 88, 90, 91, 95, 96, 98, 99, 103, 104, 106, 107, 111, 112, 114, 115, 119, 120, 122, 123

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

From Wesley Ivan Hurt, May 29 2016: (Start)

G.f.: x^2*(2+x+4*x^2+x^3)/((x-1)^2*(1+x+x^2+x^3)).

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

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

a(2k) = A047524(k), a(2k-1) = A047470(k). (End)

E.g.f.: (2 + sin(x) + cos(x) + (4*x - 5)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016

Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 21 2021

Maple

A047532:=n->2*n+(1+I)*(4*I-4+(1-I)*I^(2*n)+I^(-n)-I^(1+n))/4: seq(A047532(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Table[2n+(1+I)*(4*I-4+(1-I)*I^(2n)+I^(-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 3, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047470, A047524.

Sequence in context: A088340 A288696 A163517 * A225378 A028808 A029718

Adjacent sequences: A047529 A047530 A047531 * A047533 A047534 A047535

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved