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 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 19 04:18 EDT 2019. Contains 326109 sequences. (Running on oeis4.)