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A047493 Numbers that are congruent to {1, 4, 5, 7} mod 8. 1
1, 4, 5, 7, 9, 12, 13, 15, 17, 20, 21, 23, 25, 28, 29, 31, 33, 36, 37, 39, 41, 44, 45, 47, 49, 52, 53, 55, 57, 60, 61, 63, 65, 68, 69, 71, 73, 76, 77, 79, 81, 84, 85, 87, 89, 92, 93, 95, 97, 100, 101, 103, 105, 108, 109, 111, 113, 116, 117, 119, 121, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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*(1+3*x+x^2+2*x^3+x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015

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-3+i^(2*n)-i^(-n)-i^n)/4 where i=sqrt(-1).

a(2k) = A047535(k), a(2k-1) = A016813(k-1) for n>0. (End)

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

MAPLE

A047493:=n->(8*n-3+I^(2*n)-I^(-n)-I^n)/4: seq(A047493(n), n=1..100); # Wesley Ivan Hurt, May 26 2016

MATHEMATICA

Table[(8n-3+I^(2n)-I^(-n)-I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 26 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 5, 7, 9}, 80] (* Harvey P. Dale, May 05 2018 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 4, 5, 7]]; // Wesley Ivan Hurt, May 26 2016

CROSSREFS

Cf. A016813, A047535.

Sequence in context: A035255 A335984 A286050 * A285307 A297838 A032360

Adjacent sequences:  A047490 A047491 A047492 * A047494 A047495 A047496

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 1 09:28 EST 2020. Contains 338833 sequences. (Running on oeis4.)