A047582 - OEIS

A047582

Numbers that are congruent to {3, 5, 6, 7} mod 8.

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

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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

Sum_{n>=1} (-1)^(n+1)/a(n) = (3*sqrt(2)-2)*Pi/16 - log(2)/8 + sqrt(2)*log(3-2*sqrt(2))/16. - Amiram Eldar, Dec 26 2021

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: A216782 A328952 A072600 * A333217 A342438 A301975

Adjacent sequences: A047579 A047580 A047581 * A047583 A047584 A047585

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved