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URL: https://oeis.org/A161009

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A161009
Tribonacci left-bounded rhombic triangle.
1
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
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 A373506
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jun 02 2009
STATUS
approved