A161009 Tribonacci left-bounded rhombic triangle.

1, 1, 1, 3, 2, 1, 7, 7, 3, 1, 18, 20, 12, 4, 1, 48, 59, 40, 18, 5, 1, 132, 174, 132, 68, 25, 6, 1, 372, 517, 426, 247, 105, 33, 7, 1, 1069, 1548, 1362, 864, 415, 152, 42, 8, 1, 3121, 4670, 4332, 2956, 1561, 648, 210, 52, 9, 1, 9232, 14188, 13746, 9960, 5685, 2604, 959, 280

Offset

0,4

Links

Table of n, a(n) for n=0..62.

Sheng-Liang Yang and Yuan-Yuan Gao, The Pascal rhombus and Riordan arrays, Fib. Q., 56:4 (2018), 337-347. See Fig. 4.

Formula

Riordan array ((1/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2),(x/(1-x-x^2-x^2))*c((x/(1-x-x^2-x^3))^2)).

T(n, m) = T'(n-1, m-1)+T'(n-1,m+1)+T'(n-1, m)+T'(n-2, m)+T'(n-3,m), where T'(n, m) = T(n, m) for n >= 0 and 0 <= m< = n and T'(n, m) = 0 otherwise.

Example

Triangle begins
  1,
  1, 1,
  3, 2, 1,
  7, 7, 3, 1,
  18, 20, 12, 4, 1,
  48, 59, 40, 18, 5, 1,
  132, 174, 132, 68, 25, 6, 1,
  372, 517, 426, 247, 105, 33, 7, 1
We have, for instance, 132=59+18+40+12+3.

Maple

A161009 := proc(n, m)
    option remember;
    if m < 0 or m >n then
        0;
    elif n = m then
        1;
    else
        procname(n-1, m-1)+procname(n-1, m+1)+procname(n-1, m)+procname(n-2, m)+procname(n-3, m) ;
    end if;
end proc: # R. J. Mathar, Mar 09 2016

Crossrefs

Sequence in context: A277919 A094531 A274293 * A111960 A130462 A059380

Adjacent sequences: A161006 A161007 A161008 * A161010 A161011 A161012

Keyword

easy,nonn,tabl

Author

Paul Barry, Jun 02 2009

Status

approved