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A047532 Numbers that are congruent to {0, 2, 3, 7} mod 8. 1
0, 2, 3, 7, 8, 10, 11, 15, 16, 18, 19, 23, 24, 26, 27, 31, 32, 34, 35, 39, 40, 42, 43, 47, 48, 50, 51, 55, 56, 58, 59, 63, 64, 66, 67, 71, 72, 74, 75, 79, 80, 82, 83, 87, 88, 90, 91, 95, 96, 98, 99, 103, 104, 106, 107, 111, 112, 114, 115, 119, 120, 122, 123 (list; graph; refs; listen; history; text; internal format)
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+x+4*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) = 2*n+(1+i)*(4*i-4+(1-i)*i^(2n)+i^(-n)-i^(1+n))/4 where i=sqrt(-1).

a(2k) = A047524(k), a(2k-1) = A047470(k). (End)

E.g.f.: (2 + sin(x) + cos(x) + (4*x - 5)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016

MAPLE

A047532:=n->2*n+(1+I)*(4*I-4+(1-I)*I^(2*n)+I^(-n)-I^(1+n))/4: seq(A047532(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

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

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 2, 3, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A047470, A047524.

Sequence in context: A088340 A288696 A163517 * A225378 A028808 A029718

Adjacent sequences:  A047529 A047530 A047531 * A047533 A047534 A047535

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)