A047432 Numbers that are congruent to {0, 1, 4, 5, 6} mod 8.

0, 1, 4, 5, 6, 8, 9, 12, 13, 14, 16, 17, 20, 21, 22, 24, 25, 28, 29, 30, 32, 33, 36, 37, 38, 40, 41, 44, 45, 46, 48, 49, 52, 53, 54, 56, 57, 60, 61, 62, 64, 65, 68, 69, 70, 72, 73, 76, 77, 78, 80, 81, 84, 85, 86, 88, 89, 92, 93, 94, 96, 97, 100, 101, 102

Offset

1,3

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^2*(1+x)*(2*x^3-x^2+2*x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 07 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 - 40 + 3*(n mod 5) + 3*((n+1) mod 5) - 7*((n+2) mod 5) + 3*((n+3) mod 5) - 2*((n+4) mod 5))/25.

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

Maple

A047432:=n->8*floor(n/5)+[(0, 1, 4, 5, 6)][(n mod 5)+1]: seq(A047432(n), n=0..100); # Wesley Ivan Hurt, Aug 01 2016

Mathematica

Select[Range[0, 100], MemberQ[{0, 1, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 01 2016 *)

Prog

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

Crossrefs

Sequence in context: A354834 A089585 A089253 * A095279 A030751 A087947

Adjacent sequences: A047429 A047430 A047431 * A047433 A047434 A047435

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved