A084867 Symmetric square table, read by antidiagonals, such that antidiagonal sums form the first row shifted left: T(0,0)=1, T(0,k) = Sum_{m=0..k-1} T(m,k-1-m) when k > 0; and T(n,k) = T(n-1,k) + T(n,k-1) when n > 0, k > 0.

1, 1, 1, 2, 2, 2, 6, 4, 4, 6, 20, 10, 8, 10, 20, 68, 30, 18, 18, 30, 68, 232, 98, 48, 36, 48, 98, 232, 792, 330, 146, 84, 84, 146, 330, 792, 2704, 1122, 476, 230, 168, 230, 476, 1122, 2704, 9232, 3826, 1598, 706, 398, 398, 706, 1598, 3826, 9232, 31520, 13058, 5424

Offset: 0

Author

Paul D. Hanna, Jun 10 2003, Jun 11 2003

Keywords

• nonn
• tabl

Comments

Antidiagonal sums give A006012. Table is symmetric under transpose, so that first column equals the first row. Second row gives partial sums of first row.

Examples

			Table begins:
     1,     1,     2,     6,    20,    68,   232,    792, ...
     1,     2,     4,    10,    30,    98,   330,   1122, ...
     2,     4,     8,    18,    48,   146,   476,   1598, ...
     6,    10,    18,    36,    84,   230,   706,   2304, ...
    20,    30,    48,    84,   168,   398,  1104,   3408, ...
    68,    98,   146,   230,   398,   796,  1900,   5308, ...
   232,   330,   476,   706,  1104,  1900,  3800,   9108, ...
   792,  1122,  1598,  2304,  3408,  5308,  9108,  18216, ...
  2704,  3826,  5424,  7728, 11136, 16444, 25552,  43768, ...
  9232, 13058, 18482, 26210, 37346, 53790, 79342, 123110, ...
		

Crossrefs

Cf. A006012 (row sums), A084868 (main diagonal).

Formula

T(0,0)=1, T(0,1)=1, T(0,n) = 4*T(0,n-1) - 2*T(0,n-2) when n >= 2.