A047507 Numbers that are congruent to {0, 4, 6, 7} mod 8.

0, 4, 6, 7, 8, 12, 14, 15, 16, 20, 22, 23, 24, 28, 30, 31, 32, 36, 38, 39, 40, 44, 46, 47, 48, 52, 54, 55, 56, 60, 62, 63, 64, 68, 70, 71, 72, 76, 78, 79, 80, 84, 86, 87, 88, 92, 94, 95, 96, 100, 102, 103, 104, 108, 110, 111, 112, 116, 118, 119, 120, 124

Offset

1,2

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*(4+2*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

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

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

a(n) = (8*n-3+i^(2*n)-(1+2*i)*i^(-n)-(1-2*i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047535(k), a(2k-1) = A047451(k). (End)

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

Sum_{n>=2} (-1)^n/a(n) = (6-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 23 2021

a(n) = -A003485(-n) = a(n+4) - 8 for all n in Z. - Michael Somos, Dec 12 2023

Example

G.f. = 4*x^2 + 6*x^3 + 7*x^4 + 8*x^5 + 12*x^6 + 14*x^7 + 15*x^8 + 16*x^9 + ... - Michael Somos, Dec 12 2023

Maple

A047507:=n->(8*n-3+I^(2*n)-(1+2*I)*I^(-n)-(1-2*I)*I^n)/4: seq(A047507(n), n=1..100); # Wesley Ivan Hurt, May 27 2016

Mathematica

Table[(8n-3+I^(2n)-(1+2*I)*I^(-n)-(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
a[ n_] := 2*n - Max[0, 2 - Mod[1-n, 4]]; (* Michael Somos, Dec 12 2023 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
(PARI) {a(n) = 2*n - max(0, 2 - (1-n)%4)}; /* Michael Somos, Dec 12 2023 */

Crossrefs

Cf. A003485, A047451, A047535.

Sequence in context: A047291 A100349 A326892 * A024554 A078744 A024555

Adjacent sequences: A047504 A047505 A047506 * A047508 A047509 A047510

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved