|
Search: id:A154693
|
|
|
| A154693 |
|
Generalized Sierpinski-Pascal-Eulerian gasket triangular sequence:p = 2; q = 1; 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}]. |
|
+0
1
|
|
| 2, 3, 3, 5, 16, 5, 9, 66, 66, 9, 17, 260, 528, 260, 17, 33, 1026, 3624, 3624, 1026, 33, 65, 4080, 23820, 38656, 23820, 4080, 65, 129, 16302, 154548, 374856, 374856, 154548, 16302, 129, 257, 65260, 993344, 3529360, 4998080, 3529360, 993344, 65260, 257
(list; table; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Row sums are:A000629 :
{2, 6, 26, 150, 1082, 9366, 94586, 1091670, 14174522, 204495126, 3245265146,...}
|
|
REFERENCES
|
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)
|
|
FORMULA
|
p = 2; q = 1;
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}].
|
|
EXAMPLE
|
{2},
{3, 3},
{5, 16, 5},
{9, 66, 66, 9},
{17, 260, 528, 260, 17},
{33, 1026, 3624, 3624, 1026, 33},
{65, 4080, 23820, 38656, 23820, 4080, 65},
{129, 16302, 154548, 374856, 374856, 154548, 16302, 129},
{257, 65260, 993344, 3529360, 4998080, 3529360, 993344, 65260, 257},
{513, 261354, 6314880, 32773824, 62896992, 62896992, 32773824, 6314880, 261354, 513},
{1025, 1046504, 39685620, 299674368, 779049120, 1006351872, 779049120, 299674368, 39685620, 1046504, 1025}
|
|
MATHEMATICA
|
Clear[t, p, q, n, m]; p = 2; q = 1;
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[%]
|
|
CROSSREFS
|
A000629
Sequence in context: A053199 A045626 A154923 this_sequence A065854 A064776 A096659
Adjacent sequences: A154690 A154691 A154692 this_sequence A154694 A154695 A154696
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jan 14 2009
|
|
|
Search completed in 0.002 seconds
|
