A047427 Numbers that are congruent to {1, 3, 4, 5, 6} mod 8.

1, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 21, 22, 25, 27, 28, 29, 30, 33, 35, 36, 37, 38, 41, 43, 44, 45, 46, 49, 51, 52, 53, 54, 57, 59, 60, 61, 62, 65, 67, 68, 69, 70, 73, 75, 76, 77, 78, 81, 83, 84, 85, 86, 89, 91, 92, 93, 94, 97, 99, 100, 101, 102

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

G.f.: x*(1+2*x+x^2+x^3+x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Aug 01 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 25 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) - 7*((n+4) mod 5))/25.

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

Maple

A047427:=n->8*floor(n/5)+[(1, 3, 4, 5, 6)][(n mod 5)+1]: seq(A047427(n), n=0..100); # Wesley Ivan Hurt, Aug 01 2016

Mathematica

Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 01 2016 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 3, 4, 5, 6, 9}, 70] (* Harvey P. Dale, Dec 15 2018 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 4, 5, 6]]; // Wesley Ivan Hurt, Aug 01 2016
(PARI) a(n)=[-2, 1, 3, 4, 5][n%5+1] + n\5*8 \\ Charles R Greathouse IV, Aug 01 2016

Crossrefs

Sequence in context: A136681 A206330 A104373 * A228235 A228895 A267322

Adjacent sequences: A047424 A047425 A047426 * A047428 A047429 A047430

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved