

A130128


Triangle read by rows: T(n,k) = (n  k + 1)*2^(k1).


3



1, 2, 2, 3, 4, 4, 4, 6, 8, 8, 5, 8, 12, 16, 16, 6, 10, 16, 24, 32, 32, 7, 12, 20, 32, 48, 64, 64, 8, 14, 24, 40, 64, 96, 128, 128, 9, 16, 28, 48, 80, 128, 192, 256, 256, 10, 18, 32, 56, 96, 160, 256, 384, 512, 512, 11, 20, 36, 64, 112, 192, 320, 512, 768, 1024, 1024
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OFFSET

1,2


COMMENTS

T(n,k) is the number of paths from node 0 to odd k in a directed graph with 2n+1 vertices labeled 0, 1, ..., 2n+1 and edges leading from i to i+1 for all i, from i to i+2 for even i, and from i to i2 for odd i.  Grace Work, Mar 01 2020


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275
E. Krom and M. M. Roughan, Path Counting and Eulerian Numbers, Girls' Angle Bulletin, Vol. 13, No. 3 (2020), 810.


FORMULA

Equals A004736 * A130123 as infinite lower triangular matrices.


EXAMPLE

First few rows of the triangle are:
1;
2, 2;
3, 4, 4;
4, 6, 8, 8;
5, 8, 12, 16, 16;
6, 10, 16, 24, 32, 32;
7, 12, 20, 32, 48, 64, 64;
...


MATHEMATICA

Table[(n  k + 1)*2^(k  1), {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Mar 23 2020 *)


PROG

(PARI) T(n, k)={(n  k + 1)*2^(k1)} \\ Andrew Howroyd, Mar 01 2020


CROSSREFS

Row sums are A000295.
Cf. A004736, A130123.
Sequence in context: A273353 A259197 A309559 * A210556 A208914 A049980
Adjacent sequences: A130125 A130126 A130127 * A130129 A130130 A130131


KEYWORD

nonn,tabl,walk,changed


AUTHOR

Gary W. Adamson, May 11 2007


EXTENSIONS

Name clarified by Grace Work, Mar 01 2020
Terms a(56) and beyond from Andrew Howroyd, Mar 01 2020


STATUS

approved



