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A104580
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Tribonacci convolution triangle.
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3
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1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 7, 12, 9, 4, 1, 13, 26, 25, 14, 5, 1, 24, 56, 63, 44, 20, 6, 1, 44, 118, 153, 125, 70, 27, 7, 1, 81, 244, 359, 336, 220, 104, 35, 8, 1, 149, 499, 819, 864, 646, 357, 147, 44, 9, 1, 274, 1010, 1830, 2144, 1800, 1134, 546, 200, 54, 10, 1, 504
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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First column is A000073(n+2). Row sums are A077939. Diagonal sums are A002478.
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LINKS
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Table of n, a(n) for n=0..66.
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FORMULA
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Riordan array (1/(1-x-x^2-x^3), x/(1-x-x^2-x^3))
Contribution from Paul Barry, Jun 02 2009: (Start)
T(n, m) = 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. (End)
T(n,k) = sum(binomial(i+k,k)trinomial(i,n-k-i),i=0..n-k), where trinomial(n,k) are the trinomial coefficients (A027907) [Emanuele Munarini, Mar 15 2011]
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EXAMPLE
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Rows begin {1},{1,1},{2,2,1},{4,5,3,1},{7,12,9,4,1},...
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MAPLE
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# Uses function PMatrix from A357368. Adds column 1, 0, 0, 0, ... to the left.
PMatrix(10, n -> A000073(n+1)); # Peter Luschny, Oct 19 2022
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PROG
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(Maxima) trinomial(n, k):=coeff(expand((1+x+x^2)^n), x, k);
create_list(sum(binomial(i+k, k)*trinomial(i, n-k-i), i, 0, n-k), n, 0, 8, k, 0, n); [Emanuele Munarini, Mar 15 2011]
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CROSSREFS
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Sequence in context: A355276 A272888 A001404 * A202193 A105306 A183191
Adjacent sequences: A104577 A104578 A104579 * A104581 A104582 A104583
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Mar 16 2005
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STATUS
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approved
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