A205575 Triangle read by rows, related to Pascal's triangle, starting with rows 1; 1,0.

1, 1, 0, 2, 2, 1, 3, 5, 4, 1, 5, 12, 14, 8, 2, 8, 25, 38, 32, 15, 3, 13, 50, 94, 104, 71, 28, 5, 21, 96, 215, 293, 260, 149, 51, 8, 34, 180, 468, 756, 822, 612, 304, 92, 13, 55, 331, 980, 1828, 2346, 2136, 1376, 604, 164, 21

Offset: 0

Author

Philippe Deléham, Jan 29 2012

Keywords

• nonn
• tabl

Comments

Antidiagonal sums are in A052980, row sums are in A046717.

Similar to A091533 and to A091562. Triangle satisfying the same recurrence as A091533 and A091562, but with the initial values T(0,0) = 1, T(0,1) = 1, T(1,1) = 0.

Examples

			Triangle begins :
1
1, 0
2, 2, 1
3, 5, 4, 1
5, 12, 14, 8, 2
8, 25, 38, 32, 15, 3
13, 50, 94, 104, 71, 28, 5
		

Crossrefs

Cf. Column 0: A000045, Diagonals : A000045, A029907, A036681.

Cf. A090171, A090172, A090173, A090174, A091533, A091562 (same recurrence).

Programs

PARI

T(n,k) = {if(n<0, return(0)); if (n==0, if (k<0, return(0)); if (k==0, return(1))); if (n==1, if (k<0, return(0)); if (k==0, return(1)); if (k==1, return(0))); T(n-1,k)+T(n-1,k-1)+T(n-2,k)+T(n-2,k-1)+T(n-2,k-2);} \\ Michel Marcus, Oct 27 2021

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2) for n>=2, k>=0, with initial conditions specified by first two rows. T(0,0) = 1, T(1,0) = 1, T(1,1) = 0.

Extensions

a(46), a(48) corrected by Georg Fischer, Oct 27 2021