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A047551 Numbers that are congruent to {0, 1, 6, 7} mod 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)