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A047612 Numbers that are congruent to {0, 2, 4, 5} mod 8. 1
0, 2, 4, 5, 8, 10, 12, 13, 16, 18, 20, 21, 24, 26, 28, 29, 32, 34, 36, 37, 40, 42, 44, 45, 48, 50, 52, 53, 56, 58, 60, 61, 64, 66, 68, 69, 72, 74, 76, 77, 80, 82, 84, 85, 88, 90, 92, 93, 96, 98, 100, 101, 104, 106, 108, 109, 112, 114, 116, 117, 120, 122, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

From Bruno Berselli, Jul 18 2012: (Start)

G.f.: x^2*(2+2*x+x^2+3*x^3)/((1+x)*(1-x)^2*(1+x^2)).

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

From Wesley Ivan Hurt, Jun 02 2016: (Start)

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

a(2k) = A047617(k), a(2k-1) = A008586(k-1) for k>0. (End)

E.g.f.: (6 - cos(x) + 4*(x - 1)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, Jun 03 2016

MAPLE

A047612:=n->2*n-2-(1+I^(2*n))*(1+I^n)/4: seq(A047612(n), n=1..100); # Wesley Ivan Hurt, Jun 02 2016

MATHEMATICA

Select[Range[0, 120], MemberQ[{0, 2, 4, 5}, Mod[#, 8]] &] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {0, 2, 4, 5, 8}, 60] (* Bruno Berselli, Jul 18 2012 *)

PROG

From Bruno Berselli, Jul 18 2012: (Start)

(MAGMA) [n: n in [0..120] | n mod 8 in [0, 2, 4, 5]];

(Maxima) makelist(2*n-2-(1+(-1)^n)*(1+%i^n)/4, n, 1, 60);

(PARI) concat(0, Vec((2+2*x+x^2+3*x^3)/((1+x)*(1-x)^2*(1+x^2))+O(x^60))) (End)

CROSSREFS

Cf. A008586, A047617.

Sequence in context: A046809 A112777 A188972 * A123886 A005242 A323976

Adjacent sequences:  A047609 A047610 A047611 * A047613 A047614 A047615

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 23 00:18 EST 2019. Contains 320411 sequences. (Running on oeis4.)