A066709 - OEIS

A066709

Triangle T(r,c) of winning binary "same game" templates.

1, 0, 1, 1, 2, 1, 0, 2, 4, 1, 1, 5, 8, 5, 1, 0, 3, 14, 15, 6, 1, 1, 9, 25, 32, 21, 7, 1, 0, 4, 32, 62, 56, 28, 8, 1, 1, 14, 56, 109, 122, 84, 36, 9, 1, 0, 5, 60, 170, 242, 210, 120, 45, 10, 1, 1, 20, 105, 275, 436, 457, 330, 165, 55, 11, 1, 0, 6, 100, 375, 732, 912, 792, 495, 220, 66, 12, 1

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OFFSET

1,5

COMMENTS

T(r,c) is the number of winning templates with length r and minimum matching string length c; equivalently, ternary digits totaling r+c. For a definition and row sums 1,1,4,7,20, etc. see A066345. For antidiagonal sums 1,0,2,2,4,9, etc. see A066346.

LINKS

Table of n, a(n) for n=1..78.

Sean A. Irvine, Java program (github)

FORMULA

A035615(n) = 2 * Sum_{r=1..n-1, c=1..min(r,n-r)} T(r,c) * P(n-r,c) where P(n-r,c) = C(n-r-1,c-1) = (n-r-1)!/((n-r-c-2)!*(c-1)!).

EXAMPLE

Rows:

0,1;

1,2,1;

0,2,4,1;

1,5,8,5,1;

0,3,14,15,6,1; ...