A108356 Count, repeating multiples of 3 four times, all other numbers twice.

1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 29, 29, 30

Offset

0,3

Comments

Diagonal sums of number triangle A108358. Partial sums of A108357.

Links

Table of n, a(n) for n=0..76.

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

Formula

G.f.: (1+x^2+x^4)/(1-x-x^8+x^9).

a(n) = a(n-1) + a(n-8) - a(n-9).

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-2*k} ((C(k, j)*C(n-k-j, k)*floor((j+2)/2)) mod 2).

G.f.: (1-x^6)/((1-x)(1-x^2)(1-x^8)).

Euler transform of length 8 sequence [ 1, 1, 0, 0, 0, -1, 0, 1]. - Michael Somos, Aug 31 2006

a(n) = floor(n/2) - floor((n+2)/8) + 1. - Ridouane Oudra, Sep 08 2023

Maple

seq(floor(n/2) - floor((n+2)/8) + 1, n=0..60); # Ridouane Oudra, Sep 08 2023

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 2, 2, 3, 3, 3, 3, 4}, 80] (* Harvey P. Dale, Oct 06 2017 *)

Prog

(PARI) {a(n)=if(n<0, 0, polcoeff( (x^4+x^2+1)/(x^9-x^8-x+1)+x*O(x^n), n))} /* Michael Somos, Aug 31 2006 */

Crossrefs

Sequence in context: A356005 A262869 A342678 * A239499 A241139 A294242

Adjacent sequences: A108353 A108354 A108355 * A108357 A108358 A108359

Keyword

easy,nonn

Author

Paul Barry, May 31 2005

Status

approved