

A158815


Triangle T(n,k) read by rows, matrix product of A046899(rowreversed) * A130595.


3



1, 1, 1, 4, 1, 1, 13, 5, 1, 1, 46, 16, 6, 1, 1, 166, 58, 19, 7, 1, 1, 610, 211, 71, 22, 8, 1, 1, 2269, 781, 261, 85, 25, 9, 1, 1, 8518, 2920, 976, 316, 100, 28, 10, 1, 1, 32206, 11006, 3676, 1196, 376, 116, 31, 11, 1
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OFFSET

0,4


COMMENTS

The left factor of the matrix product is the triangle which starts
1;
2,1;
6,3,1;
20,10,4,1;
a rowreversed version of A046899, equivalent to the triangular view of the array A092392. The right factor is the inverse of the matrix A007318, which is A130595.
Swapping the two factors, A007318^(1) * A046899(rowreversed) would generate A158793.
Riordan array (f(x), g(x)) where f(x) is the g.f. of A026641 and where g(x) is the g.f. of A000957. [Philippe Deléham, Dec 05 2009]
T(n,k) is the number of nonnegative paths consisting of upsteps U=(1,1) and downsteps D=(1,1) of length 2n with k low peaks. (A low peak has its peak vertex at height 1.) Example: T(3,1)=5 counts UDUUUU, UDUUUD, UDUUDU, UDUUDD, UUDDUD.  David Callan, Nov 21 2011


LINKS

Table of n, a(n) for n=0..53.
Filippo Disanto, Andrea Frosini and Simone Rinaldi, Renzo Pinzani, The Combinatorics of Convex Permutominoes, Southeast Asian Bulletin of Mathematics (2008) 32: 883912.


FORMULA

Sum_{k=0..n} T(n,k) = A046899(n).
T(n,0) = A026641(n).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A026641(n), A000984(n), A001700(n), A000302(n) for x = 0,1,2,3 respectively. [Philippe Deléham, Dec 03 2009]


EXAMPLE

The triangle starts
1;
1, 1;
4, 1, 1;
13, 5, 1, 1;
46, 16, 6, 1, 1;
166, 58, 19, 7, 1, 1;
610, 211, 71, 22, 8, 1, 1;
2269, 781, 261, 85, 25, 9, 1, 1;
8518, 2620, 976, 316, 100, 28, 10, 1, 1;
32206, 11006, 3676, 1196, 376, 116, 31, 11, 1, 1;
122464, 41746, 13938, 4544, 1442, 441, 133, 34, 12, 1, 1;
...


CROSSREFS

Cf. A046899, A000984, A026641, A158793.
Sequence in context: A181145 A227203 A140070 * A101275 A262494 A039755
Adjacent sequences: A158812 A158813 A158814 * A158816 A158817 A158818


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson & Roger L. Bagula, Mar 27 2009


STATUS

approved



