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A047499 Numbers that are congruent to {3, 4, 5, 7} mod 8. 1
3, 4, 5, 7, 11, 12, 13, 15, 19, 20, 21, 23, 27, 28, 29, 31, 35, 36, 37, 39, 43, 44, 45, 47, 51, 52, 53, 55, 59, 60, 61, 63, 67, 68, 69, 71, 75, 76, 77, 79, 83, 84, 85, 87, 91, 92, 93, 95, 99, 100, 101, 103, 107, 108, 109, 111, 115, 116, 117, 119, 123, 124 (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*(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 27 2016: (Start)

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

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

a(2k) = A047535(k), a(2k-1) = A047621(k). (End)

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

MAPLE

A047499:=n->(8*n-1-I^(2*n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4: seq(A047499(n), n=1..100); # Wesley Ivan Hurt, May 27 2016

MATHEMATICA

Table[(8n-1-I^(2n)-(1-2*I)*I^(-n)-(1+2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [3, 4, 5, 7]]; // Wesley Ivan Hurt, May 27 2016

CROSSREFS

Cf. A047535, A047621.

Sequence in context: A057773 A020486 A091428 * A082378 A046642 A140826

Adjacent sequences:  A047496 A047497 A047498 * A047500 A047501 A047502

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 19 16:58 EDT 2019. Contains 322283 sequences. (Running on oeis4.)