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A161009
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Tribonacci left-bounded rhombic triangle.
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1
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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Sheng-Liang Yang et al., The Pascal rhombus and Riordan arrays, Fib. Q., 56:4 (2018), 337-347. See Fig. 4.
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LINKS
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Table of n, a(n) for n=0..62.
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FORMULA
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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.
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EXAMPLE
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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.
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MAPLE
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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
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CROSSREFS
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Sequence in context: A277919 A094531 A274293 * A111960 A130462 A059380
Adjacent sequences: A161006 A161007 A161008 * A161010 A161011 A161012
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Jun 02 2009
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STATUS
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approved
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