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A047582 Numbers that are congruent to {3, 5, 6, 7} mod 8. 1
3, 5, 6, 7, 11, 13, 14, 15, 19, 21, 22, 23, 27, 29, 30, 31, 35, 37, 38, 39, 43, 45, 46, 47, 51, 53, 54, 55, 59, 61, 62, 63, 67, 69, 70, 71, 75, 77, 78, 79, 83, 85, 86, 87, 91, 93, 94, 95, 99, 101, 102, 103, 107, 109, 110, 111, 115, 117, 118, 119, 123, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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

G.f.: x*(3+2*x+x^2+x^3+x^4) / ((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+1-i^(2*n)-(2-i)*i^(-n)-(2+i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047550(k), a(2k-1) = A047398(k). (End)

E.g.f.: (2 + sin(x) - 2*cos(x) + sinh(x) + 4*x*exp(x))/2. - Ilya Gutkovskiy, May 30 2016

MAPLE

A047582:=n->(8*n+1-I^(2*n)-(2-I)*I^(-n)-(2+I)*I^n)/4: seq(A047582(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Table[(8n+1-I^(2n)-(2-I)*I^(-n)-(2+I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [3, 5, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A047398, A047550.

Sequence in context: A003601 A216782 A072600 * A301975 A015814 A227026

Adjacent sequences:  A047579 A047580 A047581 * A047583 A047584 A047585

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 17 18:46 EST 2019. Contains 320222 sequences. (Running on oeis4.)