A047492 Numbers that are congruent to {0, 4, 5, 7} mod 8.

0, 4, 5, 7, 8, 12, 13, 15, 16, 20, 21, 23, 24, 28, 29, 31, 32, 36, 37, 39, 40, 44, 45, 47, 48, 52, 53, 55, 56, 60, 61, 63, 64, 68, 69, 71, 72, 76, 77, 79, 80, 84, 85, 87, 88, 92, 93, 95, 96, 100, 101, 103, 104, 108, 109, 111, 112, 116, 117, 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+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

From Wesley Ivan Hurt, May 26 2016: (Start)

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

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

a(2k) = A047535(k), a(2k-1) = A047615(k). (End)

E.g.f.: (2 - sin(x) - cos(x) + (4*x - 3)*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016

Sum_{n>=2} (-1)^n/a(n) = (2-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - Pi/8. - Amiram Eldar, Dec 23 2021

Maple

A047492:=n->2*n+(1+I)*(2*I-2+(1-I)*I^(2*n)-I^(-n)+I^(1+n))/4: seq(A047492(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

Mathematica

Table[2n+(1+I)*(2*I-2+(1-I)*I^(2n)-I^(-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)
a[n_] := 1 + n + Floor[n/2] + 2 Floor[(n - 2)/4];
Table[a[n], {n, 1, 62}] (* Peter Luschny, Dec 23 2021 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 5, 7]]; // Wesley Ivan Hurt, May 26 2016

Crossrefs

Cf. A047535, A047615.

Sequence in context: A049649 A050575 A081452 * A240161 A023629 A331840

Adjacent sequences: A047489 A047490 A047491 * A047493 A047494 A047495

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved