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Search: id:A154690
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| A154690 |
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Generalized Sierpinski-Pascal gasket triangular sequence:p = 2; q = 1; 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, 3, 3, 5, 8, 5, 9, 18, 18, 9, 17, 40, 48, 40, 17, 33, 90, 120, 120, 90, 33, 65, 204, 300, 320, 300, 204, 65, 129, 462, 756, 840, 840, 756, 462, 129, 257, 1040, 1904, 2240, 2240, 2240, 1904, 1040, 257, 513, 2322, 4752, 6048, 6048, 6048, 6048, 4752, 2322, 513
(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:A025192 :
{2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}
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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 = 1; 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},
{3, 3},
{5, 8, 5},
{9, 18, 18, 9},
{17, 40, 48, 40, 17},
{33, 90, 120, 120, 90, 33},
{65, 204, 300, 320, 300, 204, 65},
{129, 462, 756, 840, 840, 756, 462, 129},
{257, 1040, 1904, 2240, 2240, 2240, 1904, 1040, 257},
{513, 2322, 4752, 6048, 6048, 6048, 6048, 4752, 2322, 513},
{1025, 5140, 11700, 16320, 16800, 16128, 16800, 16320, 11700, 5140, 1025}
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MATHEMATICA
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Clear[t, p, q, n, m]; p = 2; q = 1;
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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A025192
Sequence in context: A035068 A153643 A053218 this_sequence A046937 A069831 A017820
Adjacent sequences: A154687 A154688 A154689 this_sequence A154691 A154692 A154693
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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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