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A154695 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) 3
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; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{2, 6, 34, 294, 3394, 48966, 847714, 17121894, 395226754, 10263450246, \ 296140575394,...}

REFERENCES

A. Lakhtakia ,R. Messier, V. K. Varadan, V. V. Varadan, "Use of combinatorial algebra for diffusion on fractals", Physical Review A, volume 34, Number 3, Sept. 1986, p. 2502 (FIG. 3).

LINKS

Table of n, a(n) for n=0..40.

FORMULA

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).

EXAMPLE

{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}

MATHEMATICA

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[%]

CROSSREFS

Sequence in context: A064776 A270592 A096659 * A154646 A046826 A323713

Adjacent sequences:  A154692 A154693 A154694 * A154696 A154697 A154698

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jan 14 2009

STATUS

approved

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Last modified February 16 14:47 EST 2019. Contains 320163 sequences. (Running on oeis4.)