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Search: id:A154698
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| A154698 |
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Generalized Sierpinski-Pascal-4th gasket triangular sequence:p = 2; q = 3; A(n,m)=(3*n - 3*k + 1)A(n - 1, k - 1) + (3*k - 2)A(n - 1, k); t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*A(n+1,m+1) |
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| 2, 5, 5, 13, 96, 13, 35, 1170, 1170, 35, 97, 12948, 39312, 12948, 97, 275, 142170, 986760, 986760, 142170, 275, 793, 1585368, 22077900, 47364480, 22077900, 1585368, 793, 2315, 18009750, 470999340, 1846449000, 1846449000, 470999340
(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, 122, 2410, 65402, 2258410, 94692602, 4670920810, 264961589882,
16990523224810, 1215217470322682,...}
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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;
A(n,m)=(3*n - 3*k + 1)A(n - 1, k - 1) + (3*k - 2)A(n - 1, k);
t(n,m)=(p^(n - m)*q^m + p^m*q^(n - m))*A(n+1,m+1)
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EXAMPLE
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{2},
{5, 5},
{13, 96, 13},
{35, 1170, 1170, 35},
{97, 12948, 39312, 12948, 97},
{275, 142170, 986760, 986760, 142170, 275},
{793, 1585368, 22077900, 47364480, 22077900, 1585368, 793},
{2315, 18009750, 470999340, 1846449000, 1846449000, 470999340, 18009750, 2315},
{6817, 207838956, 9861575616, 64802164752, 115218417600, 64802164752, 9861575616, 207838956, 6817},
{20195, 2427319170, 205220466000, 2150319921120, 6137293885920, 6137293885920, 2150319921120, 205220466000, 2427319170, 20195},
{60073, 28592134080, 4267189604340, 69149645568000, 298491222575520, 471344170438656, 298491222575520, 69149645568000, 4267189604340, 28592134080, 60073}
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MATHEMATICA
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Clear[t, p, q, n, m, A]; A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := (3*n - 3*k + 1)A[n - 1, k - 1] + (3*k - 2)A[n - 1, k];
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: A144293 A154694 A154696 this_sequence A063786 A121304 A002106
Adjacent sequences: A154695 A154696 A154697 this_sequence A154699 A154700 A154701
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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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