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Search: id:A154694
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| A154694 |
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Generalized Sierpinski-Pascal-Eulerian gasket triangular sequence:p = 2; q = 3; t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}]. |
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| 2, 5, 5, 13, 48, 13, 35, 330, 330, 35, 97, 2028, 4752, 2028, 97, 275, 11970, 54360, 54360, 11970, 275, 793, 69840, 557388, 1043712, 557388, 69840, 793, 2315, 407550, 5409180, 16868520, 16868520, 5409180, 407550, 2315, 6817, 2388516, 51011136
(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:A004123 :
{2, 10, 74, 730, 9002, 133210, 2299754, 45375130, 1007179562, 24840104410,
673895590634,...}
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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))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}].
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EXAMPLE
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{2},
{5, 5},
{13, 48, 13},
{35, 330, 330, 35},
{97, 2028, 4752, 2028, 97},
{275, 11970, 54360, 54360, 11970, 275},
{793, 69840, 557388, 1043712, 557388, 69840, 793},
{2315, 407550, 5409180, 16868520, 16868520, 5409180, 407550, 2315},
{6817, 2388516, 51011136, 247761072, 404844480, 247761072, 51011136, 2388516, 6817},
{20195, 14070570, 473616000, 3441251520, 8491093920, 8491093920, 3441251520, 473616000, 14070570, 20195},
{60073, 83276472, 4357481076, 46167480576, 164067744672, 244543504896, 164067744672, 46167480576, 4357481076, 83276472, 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))*Sum[(-1)^j*Binomial[n + 2, j]*(m - j + 1)^(n + 1), {j, 0, m + 1}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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A004123
Sequence in context: A112835 A154692 A144293 this_sequence A154696 A154698 A063786
Adjacent sequences: A154691 A154692 A154693 this_sequence A154695 A154696 A154697
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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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