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Search: id:A086606
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| A086606 |
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Triangle, read by rows, where the n-th row is the first n terms of the n-th self-convolution of the sequence formed by flattening this triangle. |
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+0
3
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| 1, 1, 2, 1, 3, 9, 1, 4, 14, 32, 1, 5, 20, 55, 140, 1, 6, 27, 86, 243, 630, 1, 7, 35, 126, 392, 1099, 2870, 1, 8, 44, 176, 598, 1808, 5048, 13256, 1, 9, 54, 237, 873, 2835, 8433, 23454, 61389, 1, 10, 65, 310, 1230, 4272, 13495, 39640, 109400, 286710, 1, 11, 77
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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The first n terms of the n-th self-convolution forms the n-th row: A={1, _1, 2, _1, 3, 9, _1, 4, 14, 32, _1, 5, 20, 55, 140, ...}; A^2={1, 2, _5, 6, 12, 28, 33, 52, 67, 164, 217, 210, 275, ...}; A^3={1, 3, 9, _16, 33, 72, 125, 222, 330, 646, 1089, 1602, ...}; A^4={1, 4, 14, 32, _73, 164, 334, 660, 1152, 2184, 3960, ...}; A^5={1, 5, 20, 55, 140, _336, 755, 1625, 3195, 6315, 12112, ...}; ...
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EXAMPLE
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Rows begin:
{1},
{1,2},
{1,3,9},
{1,4,14,32},
{1,5,20,55,140},
{1,6,27,86,243,630},
{1,7,35,126,392,1099,2870},
{1,8,44,176,598,1808,5048,13256}, ...
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CROSSREFS
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Cf. A086607 (main diagonal), A086608 (row sums).
Sequence in context: A057300 A076655 A101486 this_sequence A076112 A122454 A083782
Adjacent sequences: A086603 A086604 A086605 this_sequence A086607 A086608 A086609
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 23 2003
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