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Search: id:A084867
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| A084867 |
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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. |
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+0
2
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| 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
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OFFSET
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0,4
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COMMENT
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Anti-diagonal sums give A006012. Table is symmetric under transpose, so that first column equals the first row. Second row gives partial sums of first row.
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FORMULA
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T(0, 0)=1, T(0, 1)=1, T(0, n)=4*T(0, n-1)-2*T(0, n-2) when n>=2.
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EXAMPLE
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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, ...
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CROSSREFS
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Cf. A006012 (row sums), A084868 (main diagonal).
Sequence in context: A054274 A053695 A119918 this_sequence A099259 A131904 A038074
Adjacent sequences: A084864 A084865 A084866 this_sequence A084868 A084869 A084870
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 10 2003, Jun 11 2003
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