A047426 - OEIS

A047426

Numbers that are congruent to {0, 3, 4, 5, 6} mod 8.

0, 3, 4, 5, 6, 8, 11, 12, 13, 14, 16, 19, 20, 21, 22, 24, 27, 28, 29, 30, 32, 35, 36, 37, 38, 40, 43, 44, 45, 46, 48, 51, 52, 53, 54, 56, 59, 60, 61, 62, 64, 67, 68, 69, 70, 72, 75, 76, 77, 78, 80, 83, 84, 85, 86, 88, 91, 92, 93, 94, 96, 99, 100, 101, 102

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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^2*(3+x+x^2+x^3+2*x^4) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 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 - 30 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 7*((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-5, a(5k-4) = 8k-8. (End)

MAPLE

A047426:=n->8*floor(n/5)+[(0, 3, 4, 5, 6)][(n mod 5)+1]: seq(A047426(n), n=0..100); # Wesley Ivan Hurt, Aug 01 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 01 2016 *)

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 3, 4, 5, 6, 8}, 70] (* Harvey P. Dale, Jun 14 2020 *)

PROG

(Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4, 5, 6]]; // Wesley Ivan Hurt, Aug 01 2016

(PARI) a(n)=[-2, 0, 3, 4, 5][n%5+1] + n\5*8 \\ Charles R Greathouse IV, Aug 01 2016

CROSSREFS

Sequence in context: A100585 A023367 A291880 * A362781 A323527 A316091

Adjacent sequences: A047423 A047424 A047425 * A047427 A047428 A047429

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved