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A047409 Numbers that are congruent to {0, 1, 4, 6} mod 8. 1
0, 1, 4, 6, 8, 9, 12, 14, 16, 17, 20, 22, 24, 25, 28, 30, 32, 33, 36, 38, 40, 41, 44, 46, 48, 49, 52, 54, 56, 57, 60, 62, 64, 65, 68, 70, 72, 73, 76, 78, 80, 81, 84, 86, 88, 89, 92, 94, 96, 97, 100, 102, 104, 105, 108, 110, 112, 113, 116, 118, 120, 121, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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*(1+3*x+2*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 24 2016: (Start)

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

a(n) = (8n-9-i^(2n)+i^(-n)+i^n)/4 where i=sqrt(-1).

a(2k) = A047452(k), a(2k-1) = A008586(k-1) for k>0. (End)

E.g.f.: (4 + cos(x) + 4*(x - 1)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016

MAPLE

A047409:=n->(8*n-9-I^(2*n)+I^(-n)+I^n)/4: seq(A047409(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

MATHEMATICA

Select[Range[0, 110], MemberQ[{0, 1, 4, 6}, Mod[#, 8]]&] (* Harvey P. Dale, Sep 28 2011 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 1, 4, 6]]; // Wesley Ivan Hurt, May 24 2016

CROSSREFS

Cf. A008586, A047452.

Sequence in context: A211772 A231573 A327204 * A161576 A327446 A100425

Adjacent sequences:  A047406 A047407 A047408 * A047410 A047411 A047412

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 17:40 EDT 2019. Contains 328268 sequences. (Running on oeis4.)