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A047417 Numbers that are congruent to {2, 3, 4, 6} mod 8. 1
2, 3, 4, 6, 10, 11, 12, 14, 18, 19, 20, 22, 26, 27, 28, 30, 34, 35, 36, 38, 42, 43, 44, 46, 50, 51, 52, 54, 58, 59, 60, 62, 66, 67, 68, 70, 74, 75, 76, 78, 82, 83, 84, 86, 90, 91, 92, 94, 98, 99, 100, 102, 106, 107, 108, 110, 114, 115, 116, 118, 122, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

G.f.: x*(2+x+x^2+2*x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 25 2016: (Start)

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

a(n) = (8*n-5-i^(2*n)-(1-2*i)*i^(-n)-(1+2*i)*i^n)/4 with i=sqrt(-1).

a(2k) = A047398(k), a(2k-1) = A047463(k). (End)

E.g.f.: 2 + sin(x) - cos(x)/2 + (2*x - 1)*sinh(x) + (2*x - 3/2)*cosh(x). - Ilya Gutkovskiy, May 25 2016

MAPLE

A047417:=n->(8*n-5-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047417(n), n=1..100); # Wesley Ivan Hurt, May 25 2016

MATHEMATICA

Flatten[#+{2, 3, 4, 6}&/@(8Range[0, 20])] (* Harvey P. Dale, Dec 20 2012 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [2, 3, 4, 6]]; // Wesley Ivan Hurt, May 25 2016

CROSSREFS

Cf. A047398, A047463.

Sequence in context: A267102 A122397 A339670 * A066936 A067027 A275108

Adjacent sequences:  A047414 A047415 A047416 * A047418 A047419 A047420

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 18 13:41 EDT 2021. Contains 343088 sequences. (Running on oeis4.)