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Search: id:A156224
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| A156224 |
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Triangle read by rows:t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 3, 10, 10, 3, 3, 18, 22, 18, 3, 5, 28, 58, 58, 28, 5, 7, 46, 103, 158, 103, 46, 7, 9, 68, 187, 313, 313, 187, 68, 9, 11, 94, 306, 614, 698, 614, 306, 94, 11, 15, 133, 502, 1174, 1636, 1636, 1174, 502, 133, 15, 19, 188, 763, 2038, 3358, 4030, 3358, 2038, 763
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:
{1, 2, 6, 26, 64, 182, 470, 1154, 2748, 6920, 16762,...}
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FORMULA
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t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2.
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{3, 10, 10, 3},
{3, 18, 22, 18, 3},
{5, 28, 58, 58, 28, 5},
{7, 46, 103, 158, 103, 46, 7},
{9, 68, 187, 313, 313, 187, 68, 9},
{11, 94, 306, 614, 698, 614, 306, 94, 11},
{15, 133, 502, 1174, 1636, 1636, 1174, 502, 133, 15},
{19, 188, 763, 2038, 3358, 4030, 3358, 2038, 763, 188, 19}
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MATHEMATICA
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Clear[t, n, m];
t[n_, m_] = (Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*( PartitionsQ[n - m] + PartitionsQ[m])) - 2;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A132703 A154182 A093735 this_sequence A162516 A085471 A064221
Adjacent sequences: A156221 A156222 A156223 this_sequence A156225 A156226 A156227
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 06 2009
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