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Search: id:A154695
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| A154695 |
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Generalized Sierpinski-Pascal-MacMahon gasket triangular sequence:p = 2; q = 1; 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
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| 2, 3, 3, 5, 24, 5, 9, 138, 138, 9, 17, 760, 1840, 760, 17, 33, 4266, 20184, 20184, 4266, 33, 65, 24548, 210860, 376768, 210860, 24548, 65, 129, 143814, 2183652, 6233352, 6233352, 2183652, 143814, 129, 257, 851760, 22549616, 99411520, 149600448
(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, 6, 34, 294, 3394, 48966, 847714, 17121894, 395226754, 10263450246, \ 296140575394,...}
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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;
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},
{3, 3},
{5, 24, 5},
{9, 138, 138, 9},
{17, 760, 1840, 760, 17},
{33, 4266, 20184, 20184, 4266, 33},
{65, 24548, 210860, 376768, 210860, 24548, 65},
{129, 143814, 2183652, 6233352, 6233352, 2183652, 143814, 129},
{257, 851760, 22549616, 99411520, 149600448, 99411520, 22549616, 851760, 257},
{513, 5075634, 231836880, 1562973984, 3331838112, 3331838112, 1562973984, 231836880, 5075634, 513},
{1025, 30345532, 2370196660, 24248922944, 72553862560, 97733917952, 72553862560, 24248922944, 2370196660, 30345532, 1025}
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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 = 1;
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: A065854 A064776 A096659 this_sequence A154646 A046826 A054892
Adjacent sequences: A154692 A154693 A154694 this_sequence A154696 A154697 A154698
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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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