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A047572 Numbers that are congruent to {1, 2, 4, 5, 6, 7} mod 8. 1
1, 2, 4, 5, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 33, 34, 36, 37, 38, 39, 41, 42, 44, 45, 46, 47, 49, 50, 52, 53, 54, 55, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 81, 82, 84, 85, 86, 87 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..66.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1).

FORMULA

From Wesley Ivan Hurt, Jun 16 2016: (Start)

G.f.: x*(1+x+2*x^2+x^3+x^4+x^5+x^6) / ((x-1)^2*(1+x+x^2+x^3+x^4+x^5)).

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.

a(n) = (24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18.

a(6k) = 8k-1, a(6k-1) = 8k-2, a(6k-2) = 8k-3, a(6k-3) = 8k-4, a(6k-4) = 8k-6, a(6k-5) = 8k-7. (End)

MAPLE

A047572:=n->(24*n-9-3*cos(n*Pi)-6*cos(n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/18: seq(A047572(n), n=1..100); # Wesley Ivan Hurt, Jun 16 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{1, 2, 4, 5, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jun 16 2016 *)

PROG

(PARI) a(n)=n\6*8+[-1, 1, 2, 4, 5, 6][n%6+1] \\ Charles R Greathouse IV, Feb 24 2015

(MAGMA) [n : n in [0..100] | n mod 8 in [1, 2, 4, 5, 6, 7]]; // Wesley Ivan Hurt, Jun 16 2016

CROSSREFS

Sequence in context: A188033 A187485 A039052 * A003233 A218544 A286045

Adjacent sequences:  A047569 A047570 A047571 * A047573 A047574 A047575

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 13 08:34 EDT 2020. Contains 336442 sequences. (Running on oeis4.)