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A047533 Numbers that are congruent to {1, 2, 3, 7} mod 8. 1
1, 2, 3, 7, 9, 10, 11, 15, 17, 18, 19, 23, 25, 26, 27, 31, 33, 34, 35, 39, 41, 42, 43, 47, 49, 50, 51, 55, 57, 58, 59, 63, 65, 66, 67, 71, 73, 74, 75, 79, 81, 82, 83, 87, 89, 90, 91, 95, 97, 98, 99, 103, 105, 106, 107, 111, 113, 114, 115, 119, 121, 122, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, 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 Wesley Ivan Hurt, May 29 2016: (Start)

G.f.: x*(1+x+x^2+4*x^3+x^4) / ((x-1)^2*(1+x+x^2+x^3)).

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

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

a(2k) = A047524(k), a(2k-1) = A047471(k). (End)

E.g.f.: (2 + 2*sin(x) + cos(x) + 4*(x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016

MAPLE

A047533:=n->(8*n-7+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047533(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Table[(8n-7+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 2, 3, 7, 9}, 50] (* G. C. Greubel, May 29 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 2, 3, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A047471, A047524.

Sequence in context: A323384 A140221 A046668 * A060525 A152863 A047359

Adjacent sequences:  A047530 A047531 A047532 * A047534 A047535 A047536

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 13 07:45 EDT 2021. Contains 344981 sequences. (Running on oeis4.)