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Search: id:A154692
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| A154692 |
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Generalized Sierpinski-Pascal gasket triangular sequence:p = 2; q = 3; t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*Binomial[n, m]. |
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1
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| 2, 5, 5, 13, 24, 13, 35, 90, 90, 35, 97, 312, 432, 312, 97, 275, 1050, 1800, 1800, 1050, 275, 793, 3492, 7020, 8640, 7020, 3492, 793, 2315, 11550, 26460, 37800, 37800, 26460, 11550, 2315, 6817, 38064, 97776, 157248, 181440, 157248, 97776, 38064
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:A020729 :
{2, 10, 50, 250, 1250, 6250, 31250, 156250, 781250, 3906250, 19531250,...}
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REFERENCES
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A. Lakhtakia,R. Messier, V.K. Varadan,V.V. Varadan, "Use of combinatorial algebra for diffusion on fractals",Physical Review A, volume34, Number3, Sept 1986,page 2502, (FIG. 3)
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FORMULA
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p = 2; q = 3; t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*Binomial[n, m].
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EXAMPLE
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{2},
{5, 5},
{13, 24, 13},
{35, 90, 90, 35},
{97, 312, 432, 312, 97},
{275, 1050, 1800, 1800, 1050, 275},
{793, 3492, 7020, 8640, 7020, 3492, 793},
{2315, 11550, 26460, 37800, 37800, 26460, 11550, 2315},
{6817, 38064, 97776, 157248, 181440, 157248, 97776, 38064, 6817},
{20195, 125010, 356400, 635040, 816480, 816480, 635040, 356400, 125010, 20195},
{60073, 409020, 1284660, 2514240, 3538080, 3919104, 3538080, 2514240, 1284660, 409020, 60073}
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MATHEMATICA
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Clear[t, p, q, n, m]; p = 2; q = 3;
t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*Binomial[n, m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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A020729
Sequence in context: A124201 A100953 A112835 this_sequence A144293 A154694 A154696
Adjacent sequences: A154689 A154690 A154691 this_sequence A154693 A154694 A154695
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jan 14 2009
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