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A047411 Numbers that are congruent to {1, 2, 4, 6} mod 8. 1
1, 2, 4, 6, 9, 10, 12, 14, 17, 18, 20, 22, 25, 26, 28, 30, 33, 34, 36, 38, 41, 42, 44, 46, 49, 50, 52, 54, 57, 58, 60, 62, 65, 66, 68, 70, 73, 74, 76, 78, 81, 82, 84, 86, 89, 90, 92, 94, 97, 98, 100, 102, 105, 106, 108, 110, 113, 114, 116, 118, 121, 122, 124, 126, 129, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

FORMULA

From R. J. Mathar, Mar 10 2008: (Start)

a(n) = a(n-4)+8.

O.g.f.: 2/(-1+x)^2+1/(2(x^2+1))+7/(4(-1+x))+1/(4(x+1)). (End)

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5. - R. J. Mathar, Feb 11 2010

From Wesley Ivan Hurt, May 22 2016:

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

a(2n+2) = A016825(n) n>0, a(2n-1) = A047461(n). (End)

E.g.f.: (4 + sin(x) + (4*x - 3)*sinh(x) + 4*(x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 23 2016

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

MAPLE

A047411 := proc(n) if n <= 4 then op(n, [1, 2, 4, 6]); else procname(n-4)+8; end if; end proc: seq(A047411(n), n=1..99); # R. J. Mathar, Feb 11 2010

MATHEMATICA

Table[(8n-7-I^(2n)+I^(1-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 22 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 4, 6, 9}, 50] (* G. C. Greubel, May 23 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 2, 4, 6]]; // Wesley Ivan Hurt, May 22 2016

CROSSREFS

Cf. A016825, A047461.

Sequence in context: A228359 A156165 A024968 * A288623 A138972 A050110

Adjacent sequences:  A047408 A047409 A047410 * A047412 A047413 A047414

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended by R. J. Mathar, Feb 11 2010

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)