

A152250


Eigentriangle, row sums = A001850, the Delannoy numbers.


2



1, 2, 1, 8, 2, 3, 36, 8, 6, 13, 172, 36, 24, 26, 63, 852, 172, 108, 104, 126, 321, 4324, 852, 516, 468, 504, 642, 1683, 22332, 4324, 2556, 2236, 2268, 2568, 3366, 8989, 116876, 22332, 12972, 11076, 10836, 11556, 13464, 17978, 48639
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OFFSET

0,2


COMMENTS

Row sums = A001850, the Delannoy numbers: (1, 3, 13, 63, 321,...).
Sum of nth row terms = rightmost term of next row.


LINKS

Table of n, a(n) for n=0..44.
M. Dziemianczuk, Generalizing Delannoy numbers via counting weighted lattice paths, INTEGERS, 13 (2013), #A54.
M. Dziemianczuk, On Directed Lattice Paths With Additional Vertical Steps, arXiv preprint arXiv:1410.5747, 2014


FORMULA

Triangle read by rows, M*Q. M = an infinite lower triangular matrix with A109980 in every column: (1, 2, 8, 36, 172,...); Q = a matrix with A001850 prefaced with a "1" as the main diagonal: (1, 1, 3, 13, 63, 321,...) and the rest zeros.


EXAMPLE

First few rows of the triangle =
1;
2, 1;
8, 2, 3;
36, 8, 6, 13;
172, 36, 24, 26, 63;
852, 172, 108, 104, 126, 321;
4324, 852, 516, 468, 504, 642, 1683;
22332, 4324, 2556, 2236, 2268, 2568, 3366, 8989;
116876, 22332, 12972, 11076, 10836, 11556, 13464, 17978, 48639;
...
Row 3 = (36, 8, 6, 13) = termwise products of (36, 8, 2, 1) and (1, 1, 3, 13).


CROSSREFS

Cf. A001850, A109980.
Sequence in context: A046740 A253583 A130562 * A154175 A257777 A011208
Adjacent sequences: A152247 A152248 A152249 * A152251 A152252 A152253


KEYWORD

eigen,nonn,tabl


AUTHOR

Gary W. Adamson, Nov 30 2008


STATUS

approved



