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A105147
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Triangular array read by rows: T(n,k) = number of compositions of n having smallest part equal to k.
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4
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1, 1, 1, 3, 0, 1, 6, 1, 0, 1, 13, 2, 0, 0, 1, 27, 3, 1, 0, 0, 1, 56, 5, 2, 0, 0, 0, 1, 115, 9, 2, 1, 0, 0, 0, 1, 235, 15, 3, 2, 0, 0, 0, 0, 1, 478, 25, 5, 2, 1, 0, 0, 0, 0, 1, 969, 42, 8, 2, 2, 0, 0, 0, 0, 0, 1, 1959, 70, 12, 3, 2, 1, 0, 0, 0, 0, 0, 1, 3952, 116, 18, 5, 2, 2, 0, 0, 0, 0, 0, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| Alois P. Heinz, Rows n = 1..141, flattened
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FORMULA
| G.f. for k-th column: (1-x)^2*x^k/((1-x-x^k)*(1-x-x^(k+1))).
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EXAMPLE
| 1;
1, 1;
3, 0, 1;
6, 1, 0, 1;
13, 2, 0, 0, 1;
27, 3, 1, 0, 0, 1;
56, 5, 2, 0, 0, 0, 1;
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MAPLE
| p:= (t, l)-> zip ((x, y)->x+y, t, l, 0):
b:= proc(n) option remember; local j, t, h, m, s;
t:= [0$(n-1), 1];
for j to n-1 do
h:= b(n-j);
m:= nops(h);
t:= p(p(t, [seq(h[i], i=1..min(j, m))]),
[0$(j-1), add(h[i], i=j+1..m)])
od; t
end:
T:= n-> b(n)[]:
seq (T(n), n=1..15); # Alois P. Heinz, Nov 13 2011
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CROSSREFS
| Cf. A048004.
Row sums give: A000079(n-1), columns k=1, 2 give: A099036(n-1), A200047. - Alois P. Heinz, Nov 13 2011
Sequence in context: A119925 A102765 A129684 * A111924 A100485 A143397
Adjacent sequences: A105144 A105145 A105146 * A105148 A105149 A105150
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 10 2005
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