A047553 Numbers that are congruent to {0, 2, 6, 7} mod 8.

0, 2, 6, 7, 8, 10, 14, 15, 16, 18, 22, 23, 24, 26, 30, 31, 32, 34, 38, 39, 40, 42, 46, 47, 48, 50, 54, 55, 56, 58, 62, 63, 64, 66, 70, 71, 72, 74, 78, 79, 80, 82, 86, 87, 88, 90, 94, 95, 96, 98, 102, 103, 104, 106, 110, 111, 112, 114, 118, 119, 120, 122, 126

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+4*x+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) = (8*n-5-i^(2*n)+(1-2*i)*i^(-n)+(1+2*i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047524(k), a(2k-1) = A047451(k). (End)

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

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

Maple

A047553:=n->(8*n-5-I^(2*n)+(1-2*I)*I^(-n)+(1+2*I)*I^n)/4: seq(A047553(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 2, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Aug 09 2013 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047451, A047524.

Sequence in context: A028735 A267541 A325465 * A139418 A190212 A327179

Adjacent sequences: A047550 A047551 A047552 * A047554 A047555 A047556

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved