A047512 Numbers that are congruent to {1, 2, 4, 6, 7} mod 8.

1, 2, 4, 6, 7, 9, 10, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 62, 63, 65, 66, 68, 70, 71, 73, 74, 76, 78, 79, 81, 82, 84, 86, 87, 89, 90, 92, 94, 95, 97, 98, 100, 102, 103

Offset

1,2

Links

Table of n, a(n) for n=1..65.

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

Formula

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

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

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6. (End)

From Wesley Ivan Hurt, Jul 28 2016: (Start)

a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 20 + 3*(n mod 5) - 2*((n+1) mod 5) - 2*((n+2) mod 5) + 3*((n+3) mod 5) - 2*((n+4) mod 5))/25.

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

Maple

A047512:=n->8*floor(n/5)+[(1, 2, 4, 6, 7)][(n mod 5)+1]: seq(A047512(n), n=0..100); # Wesley Ivan Hurt, Jul 28 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 2, 4, 6, 7}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Jul 28 2016 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 4, 6, 7]]; // Wesley Ivan Hurt, Jul 28 2016
(PARI) a(n)=[-1, 1, 2, 4, 6][n%5+1] + n\5*8 \\ Charles R Greathouse IV, Jul 29 2016

Crossrefs

Sequence in context: A247000 A213356 A079393 * A026273 A184658 A247910

Adjacent sequences: A047509 A047510 A047511 * A047513 A047514 A047515

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved