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

0,4

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.

Links

Table of n, a(n) for n=0..57.

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.

Example

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).

Sequence in context: A208659 A209752 A119918 * A194949 A227550 A286384

Adjacent sequences: A084864 A084865 A084866 * A084868 A084869 A084870

Keyword

nonn,tabl

Author

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

Status

approved