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A047565 Numbers that are congruent to {0, 1, 3, 4, 5, 6, 7} mod 8. 1
0, 1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

FORMULA

From Chai Wah Wu, May 30 2016: (Start)

G.f.: x^2*(x^6 + x^5 + x^4 + x^3 + x^2 + 2*x + 1)/(x^8 - x^7 - x + 1).

a(n) = a(n-1) + a(n-7) - a(n-8) for n>8. (End)

From Wesley Ivan Hurt, Jul 21 2016: (Start)

a(n) = a(n-7) + 8 for n>7.

a(n) = (56*n - 42 + (n mod 7) + ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) - 6*((n+4) mod 7) + ((n+5) mod 7) + ((n+6) mod 7))/49.

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

MAPLE

A047565:=n->8*floor(n/7)+[0, 1, 3, 4, 5, 6, 7][(n mod 7)+1]: seq(A047565(n), n=0..100); # Wesley Ivan Hurt, Jul 21 2016

MATHEMATICA

LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 1, 3, 4, 5, 6, 7, 8} , 50] (* G. C. Greubel, May 30 2016 *)

Select[Range[0, 200], MemberQ[{0, 1, 3, 4, 5, 6, 7}, Mod[#, 8] &]] (* Vincenzo Librandi, May 30 2016 *)

PROG

(MAGMA) [n: n in [0..150] | n mod 8 in [0, 1, 3, 4, 5, 6, 7]]; // Vincenzo Librandi, May 30 2016

CROSSREFS

Sequence in context: A137937 A260580 A297468 * A026466 A304806 A304810

Adjacent sequences:  A047562 A047563 A047564 * A047566 A047567 A047568

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)