A047551 - OEIS

A047551

Numbers that are congruent to {0, 1, 6, 7} mod 8.

0, 1, 6, 7, 8, 9, 14, 15, 16, 17, 22, 23, 24, 25, 30, 31, 32, 33, 38, 39, 40, 41, 46, 47, 48, 49, 54, 55, 56, 57, 62, 63, 64, 65, 70, 71, 72, 73, 78, 79, 80, 81, 86, 87, 88, 89, 94, 95, 96, 97, 102, 103, 104, 105, 110, 111, 112, 113, 118, 119, 120, 121, 126

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OFFSET

1,3

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

a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=1, b(1)=6 and b(k)=2^(k+1) for k>1. - Philippe Deléham, Oct 19 2011

a(n) = 2n - A010873(n+1). - Wesley Ivan Hurt, Jul 07 2013

G.f.: x^2*(1+5*x+x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 14 2013

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

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

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

a(2k) = A047522(k), a(2k-1) = A047451(k). (End)

E.g.f.: 1 - sin(x) + cos(x) + (2*x - 1)*sinh(x) + 2*(x - 1)*cosh(x). - Ilya Gutkovskiy, May 29 2016

Sum_{n>=2} (-1)^n/a(n) = Pi/16 + (5-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4. - Amiram Eldar, Dec 20 2021

MAPLE

A047551:=n->(4*n-3-I^(2*n)+(1-I)*I^(-n)+(1+I)*I^n)/2: seq(A047551(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Table[(4n-3-I^(2n)+(1-I)*I^(-n)+(1+I)*I^n)/2, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [0, 1, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A010873, A030308, A047451, A047522.

Sequence in context: A177106 A269101 A037366 * A010755 A063971 A191879

Adjacent sequences: A047548 A047549 A047550 * A047552 A047553 A047554

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved