A066346 -id:A066346 - cp's OEIS frontend

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

Offset: 1

Frank Ellermann, Dec 31 2001

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.

			Rows:
1;
0,1;
1,2,1;
0,2,4,1;
1,5,8,5,1;
0,3,14,15,6,1; ...
a(17) = T(6,2) = 3 winning templates with length 6 and total 8 = 6+2: 211211, 121121, 112112.
A035615(6) = 2*( 1*1+0*1+1*3+1*1+2*2+1*1+1*1+0*1+2*1+1*1 ) = 2*13 = 26.

Sean A. Irvine, Java program (github)

Cf. A035615, A066345, A066346, A007318.

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)!).

More terms from Sean A. Irvine, Nov 03 2023

cp's OEIS Frontend

A066709 Triangle T(r,c) of winning binary "same game" templates.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

Extensions