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Search: id:A154696
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| A154696 |
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Generalized Sierpinski-Pascal-MacMahon gasket triangular sequence:p = 2; q = 3; p(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; t(n,m)=Coefficients(p(x,n)); t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*t(n,m) |
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| 2, 5, 5, 13, 72, 13, 35, 690, 690, 35, 97, 5928, 16560, 5928, 97, 275, 49770, 302760, 302760, 49770, 275, 793, 420204, 4934124, 10172736, 4934124, 420204, 793, 2315, 3595350, 76427820, 280500840, 280500840, 76427820, 3595350, 2315, 6817
(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:
{2, 10, 98, 1450, 28610, 705610, 20882978, 721052650, 28453354370,
1263142915210, 62305874905058,...}
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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;
p(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2];
t(n,m)=Coefficients(p(x,n));
t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*t(n,m)
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EXAMPLE
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{2},
{5, 5},
{13, 72, 13},
{35, 690, 690, 35},
{97, 5928, 16560, 5928, 97},
{275, 49770, 302760, 302760, 49770, 275},
{793, 420204, 4934124, 10172736, 4934124, 420204, 793},
{2315, 3595350, 76427820, 280500840, 280500840, 76427820, 3595350, 2315},
{6817, 31174416, 1157989104, 6978688704, 12117636288, 6978688704, 1157989104, 31174416, 6817},
{20195, 273257970, 17387766000, 164112268320, 449798145120, 449798145120, 164112268320, 17387766000, 273257970, 20195},
{60073, 2414772276, 260247593268, 3735760540608, 15279843455136, 23749342062336, 15279843455136, 3735760540608, 260247593268, 2414772276, 60073}
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MATHEMATICA
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Clear[t, p, q, n, m, a];
p[x_, n_] = 2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2];
a = Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
p = 2; q = 3;
t[n_, m_] := (p^(n - m)*q^m + p^m*q^(n - m))*a[[n + 1]][[m + 1]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A154692 A144293 A154694 this_sequence A154698 A063786 A121304
Adjacent sequences: A154693 A154694 A154695 this_sequence A154697 A154698 A154699
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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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