A047575 - OEIS

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A047575

Numbers that are congruent to {0, 5, 6, 7} mod 8.

0, 5, 6, 7, 8, 13, 14, 15, 16, 21, 22, 23, 24, 29, 30, 31, 32, 37, 38, 39, 40, 45, 46, 47, 48, 53, 54, 55, 56, 61, 62, 63, 64, 69, 70, 71, 72, 77, 78, 79, 80, 85, 86, 87, 88, 93, 94, 95, 96, 101, 102, 103, 104, 109, 110, 111, 112, 117, 118, 119, 120, 125

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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^2*(5+x+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) = (4*n-1+i^(2*n)-(1+i)*i^(-n)-(1-i)*i^n)/2 where i=sqrt(-1).

a(2k) = A047550(k), a(2k-1) = A047451(k). (End)

E.g.f.: 1 - sin(x) - cos(x) - sinh(x) + 2*x*exp(x). - Ilya Gutkovskiy, May 30 2016

Sum_{n>=2} (-1)^n/a(n) = 5*log(2)/8 - (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 23 2021

MAPLE

A047575:=n->(4*n-1+I^(2*n)-(1+I)*I^(-n)-(1-I)*I^n)/2: seq(A047575(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Select[Range[0, 120], MemberQ[{0, 5, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jun 30 2011 *)

PROG

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

CROSSREFS

Cf. A047451, A047550.

Sequence in context: A080703 A284682 A171405 * A014097 A219331 A229862

Adjacent sequences: A047572 A047573 A047574 * A047576 A047577 A047578

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved