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A047558 Numbers that are congruent to {1, 3, 6, 7} mod 8. 1
1, 3, 6, 7, 9, 11, 14, 15, 17, 19, 22, 23, 25, 27, 30, 31, 33, 35, 38, 39, 41, 43, 46, 47, 49, 51, 54, 55, 57, 59, 62, 63, 65, 67, 70, 71, 73, 75, 78, 79, 81, 83, 86, 87, 89, 91, 94, 95, 97, 99, 102, 103, 105, 107, 110, 111, 113, 115, 118, 119, 121, 123, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..63.

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

a(2k) = A004767(k-1) for k>0, a(2k-1) = A047452(k). (End)

E.g.f.: (2 - sin(x) + (4*x - 1)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 30 2016

MAPLE

A047558:=n->(8*n-3-I^(2*n)-I^(1-n)+I^(1+n))/4: seq(A047558(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

MATHEMATICA

Select[Range[150], MemberQ[{1, 3, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Jul 31 2014 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 3, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A004767, A047452.

Sequence in context: A026406 A289182 A188974 * A160217 A228014 A188971

Adjacent sequences:  A047555 A047556 A047557 * A047559 A047560 A047561

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 23 04:46 EDT 2019. Contains 321422 sequences. (Running on oeis4.)