A164585 Generalized rhombic triangle.

1, 0, 1, 1, 1, 1, 3, 2, 2, 1, 3, 8, 4, 3, 1, 11, 13, 15, 7, 4, 1, 24, 35, 33, 25, 11, 5, 1, 51, 91, 84, 66, 39, 16, 6, 1, 137, 205, 232, 174, 116, 58, 22, 7, 1, 320, 539, 569, 496, 325, 188, 83, 29, 8, 1, 795, 1349, 1498, 1308, 955, 562, 288, 115, 37, 9, 1

Offset

0,7

Comments

Row sums are A164586.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = T(n-1,k-1)+T(n-2,k-1)+T(n-3,k)+T(n-2,k+1)+T(n-1,k+1); T(n,n) = 1.

Riordan array ((1/(1-x^3))*c((x(1+x)/(1-x^3))^2), (x(1+x)/(1-x^3))*c((x(1+x)/(1-x^3))^2)), c(x) the g.f. of A000108.

Example

Triangle begins
1,
0, 1,
1, 1, 1,
3, 2, 2, 1,
3, 8, 4, 3, 1,
11, 13, 15, 7, 4, 1,
24, 35, 33, 25, 11, 5, 1,
51, 91, 84, 66, 39, 16, 6, 1,
137, 205, 232, 174, 116, 58, 22, 7, 1,
320, 539, 569, 496, 325, 188, 83, 29, 8, 1

Maple

A164585 := proc(n, k)
    option remember;
    if k < 0 or k> n or n < 0 then
        0;
    elif k = n then
        1 ;
    else
        procname(n-1, k-1)
        +procname(n-2, k-1)
        +procname(n-3, k)
        +procname(n-2, k+1)
        +procname(n-1, k+1) ;
    end if;
end proc:
seq(seq(A164585(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Feb 10 2015

Crossrefs

Sequence in context: A329873 A068448 A054081 * A200996 A154364 A183043

Adjacent sequences: A164582 A164583 A164584 * A164586 A164587 A164588

Keyword

easy,nonn,tabl

Author

Paul Barry, Aug 17 2009

Status

approved