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A276696 Triangle read by rows, T(n,k) = T(n-1, k-1) + T(n-2, k) if k is odd, T(n-1, k-1) + T(n-1, k) if k is even, for k<=0<=n and n>=2 with T(0,0)=T(1,0)=T(1,1)=0 and T(n,k)=0 when k>n, k<0, or n<0. 0
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 5, 3, 1, 1, 3, 9, 8, 8, 3, 1, 1, 4, 12, 14, 16, 9, 4, 1, 1, 4, 16, 20, 30, 19, 13, 4, 1, 1, 5, 20, 30, 50, 39, 32, 14, 5, 1, 1, 5, 25, 40, 80, 69, 71, 36, 19, 5, 1, 1, 6, 30, 55, 120, 119, 140, 85, 55, 20, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

This is the triangle frst(n,k) in the Ehrenborg and Readdy link. See Definition 3.1 and Table 1.

LINKS

Table of n, a(n) for n=0..77.

Richard Ehrenborg, Margaret A. Readdy, The Gaussian coefficient revisited, arXiv:1609.03216 [math.CO], 2016.

EXAMPLE

Triangle starts:

1;

1, 1;

1, 1, 1;

1, 2, 2, 1;

1, 2, 4, 2, 1;

1, 3, 6, 5, 3, 1;

1, 3, 9, 8, 8, 3, 1;

...

PROG

(PARI) frst(n, k) = if ((k>n) || (n<0) || (k<0), 0, if (n<=2, 1, if (k==0, 1, if (k%2, frst(n-1, k-1) + frst(n-2, k), frst(n-1, k-1) + frst(n-1, k)))));

tf(nn) = for (n=0, nn, for (k=0, n, print1(frst(n, k), ", "); ); print(); );

CROSSREFS

Cf. A169623 (the triangle er).

Sequence in context: A199204 A262750 A075402 * A220777 A088855 A034851

Adjacent sequences:  A276693 A276694 A276695 * A276697 A276698 A276699

KEYWORD

nonn,tabl

AUTHOR

Michel Marcus, Sep 14 2016

STATUS

approved

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Last modified February 19 15:44 EST 2018. Contains 299356 sequences. (Running on oeis4.)