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 A156224 Triangle read by rows:t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2. 0
 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; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 6, 26, 64, 182, 470, 1154, 2748, 6920, 16762,...} LINKS FORMULA t(n,m)=(Binomial[n, m]*PartitionsQ[n] + Binomial[n, n - m]*(PartitionsQ[ n - m] + PartitionsQ[m])) - 2. EXAMPLE {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} MATHEMATICA 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[%] CROSSREFS Sequence in context: A321121 A093735 A298918 * A162516 A193793 A301510 Adjacent sequences:  A156221 A156222 A156223 * A156225 A156226 A156227 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 06 2009 STATUS approved

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Last modified October 14 12:25 EDT 2019. Contains 328006 sequences. (Running on oeis4.)