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A130128 Triangle read by rows: T(n,k) = (n - k + 1)*2^(k-1). 5

%I

%S 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,

%T 64,8,14,24,40,64,96,128,128,9,16,28,48,80,128,192,256,256,10,18,32,

%U 56,96,160,256,384,512,512,11,20,36,64,112,192,320,512,768,1024,1024

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

%C 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 i-2 for odd i. - _Grace Work_, Mar 01 2020

%H Andrew Howroyd, <a href="/A130128/b130128.txt">Table of n, a(n) for n = 1..1275</a>

%H E. Krom and M. M. Roughan, <a href="http://girlsangle.org/page/bulletin-archive/GABv13n03E.pdf">Path Counting and Eulerian Numbers</a>, Girls' Angle Bulletin, Vol. 13, No. 3 (2020), 8-10.

%F Equals A004736 * A130123 as infinite lower triangular matrices.

%e First few rows of the triangle are:

%e 1;

%e 2, 2;

%e 3, 4, 4;

%e 4, 6, 8, 8;

%e 5, 8, 12, 16, 16;

%e 6, 10, 16, 24, 32, 32;

%e 7, 12, 20, 32, 48, 64, 64;

%e ...

%t Table[(n - k + 1)*2^(k - 1), {n, 11}, {k, n}] // Flatten (* _Michael De Vlieger_, Mar 23 2020 *)

%o (PARI) T(n,k)={(n - k + 1)*2^(k-1)} \\ _Andrew Howroyd_, Mar 01 2020

%Y Row sums are A000295.

%Y Cf. A004736, A130123.

%K nonn,tabl,walk

%O 1,2

%A _Gary W. Adamson_, May 11 2007

%E Name clarified by _Grace Work_, Mar 01 2020

%E Terms a(56) and beyond from _Andrew Howroyd_, Mar 01 2020

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Last modified July 5 16:07 EDT 2020. Contains 335473 sequences. (Running on oeis4.)