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A047576 Numbers that are congruent to {1, 5, 6, 7} mod 8. 1
1, 5, 6, 7, 9, 13, 14, 15, 17, 21, 22, 23, 25, 29, 30, 31, 33, 37, 38, 39, 41, 45, 46, 47, 49, 53, 54, 55, 57, 61, 62, 63, 65, 69, 70, 71, 73, 77, 78, 79, 81, 85, 86, 87, 89, 93, 94, 95, 97, 101, 102, 103, 105, 109, 110, 111, 113, 117, 118, 119, 121, 125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, 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+4*x+x^2+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-1+i^(2*n)-(2+i)*i^(-n)-(2-i)*i^n)/4 where i=sqrt(-1).

a(2k) = A047550(k), a(2k-1) = A047452(k). (End)

E.g.f.: (2 - sin(x) - 2*cos(x) - sinh(x) + 4*x*exp(x))/2. - Ilya Gutkovskiy, May 30 2016

MAPLE

A047576:=n->(8*n-1+I^(2*n)-(2+I)*I^(-n)-(2-I)*I^n)/4: seq(A047576(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Flatten[#+{1, 5, 6, 7}&/@(8Range[0, 20])] (* Harvey P. Dale, Apr 22 2011 *)

Select[Range[100], MemberQ[{1, 5, 6, 7}, Mod[#, 8]] &] (* Vincenzo Librandi, May 30 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 5, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A047452, A047550.

Sequence in context: A241203 A279001 A080708 * A123123 A092858 A138966

Adjacent sequences:  A047573 A047574 A047575 * A047577 A047578 A047579

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)