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A047441 Numbers that are congruent to {0, 2, 5, 6} mod 8. 1
0, 2, 5, 6, 8, 10, 13, 14, 16, 18, 21, 22, 24, 26, 29, 30, 32, 34, 37, 38, 40, 42, 45, 46, 48, 50, 53, 54, 56, 58, 61, 62, 64, 66, 69, 70, 72, 74, 77, 78, 80, 82, 85, 86, 88, 90, 93, 94, 96, 98, 101, 102, 104, 106, 109, 110, 112, 114, 117, 118, 120, 122, 125 (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

G.f.: x^2*(2+3*x+x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 2011

From Wesley Ivan Hurt, May 26 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-7-i^(2*n)-i^(1-n)+i^(1+n))/4 where i=sqrt(-1).

a(2k) = A130824(k) k>0, a(2k-1) = A047615(k). (End)

E.g.f.: (4 - sin(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016

a(n) = (8*n-7-cos(n*Pi)-2*sin(n*Pi/2))/4. - Wesley Ivan Hurt, Oct 05 2017

MAPLE

A047441:=n->(8*n-7-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047441(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

MATHEMATICA

Table[(8n-7-I^(2n)-I^(1-n)+I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 2, 5, 6]]; // Wesley Ivan Hurt, May 26 2016

CROSSREFS

Cf. A047615, A130824.

Sequence in context: A187476 A121411 A224889 * A284777 A081083 A288635

Adjacent sequences:  A047438 A047439 A047440 * A047442 A047443 A047444

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 25 00:59 EDT 2019. Contains 323534 sequences. (Running on oeis4.)