|
Search: id:A154915
|
|
|
| A154915 |
|
A triangular sequence: p = 2; q = 1; t(n,m) = (p^(n - m)*q^m + p^m*q^( n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]). |
|
+0
1
|
|
| 4, 3, 3, 5, 8, 5, 9, 24, 24, 9, 17, 70, 112, 70, 17, 33, 198, 480, 480, 198, 33, 65, 544, 1920, 2880, 1920, 544, 65, 129, 1452, 7308, 15624, 15624, 7308, 1452, 129, 257, 3770, 26724, 80640, 108864, 80640, 26724, 3770, 257, 513, 9546, 94644, 408312, 706608
(list; table; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Row sums are:
{4, 6, 18, 66, 286, 1422, 7938, 49026, 331646, 2439246, 19394498,..}.
Fractal Plot:
a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 243}];
b = Table[If[m <= n, 3 - Mod[a[[n]][[m]], 3], 0], {m, 1, Length[a]}, {n, 1, Length[a]}];
ListDensityPlot[b, Mesh -> False, Frame -> False, AspectRatio -> Automatic, ColorFunction -> (Hue[2# ] &)]
|
|
FORMULA
|
p = 2; q = 1;
t(n,m) = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]).
|
|
EXAMPLE
|
{4},
{3, 3},
{5, 8, 5},
{9, 24, 24, 9},
{17, 70, 112, 70, 17},
{33, 198, 480, 480, 198, 33},
{65, 544, 1920, 2880, 1920, 544, 65},
{129, 1452, 7308, 15624, 15624, 7308, 1452, 129},
{257, 3770, 26724, 80640, 108864, 80640, 26724, 3770, 257},
{513, 9546, 94644, 408312, 706608, 706608, 408312, 94644, 9546, 513},
{1025, 23644, 327860, 2068560, 4554560, 5443200, 4554560, 2068560, 327860, 23644, 1025}
|
|
MATHEMATICA
|
Clear[t, p, q, n, m, a];
p = 2; q = 1;
t[n_, m_] = (p^(n - m)*q^m + p^m*q^(n - m))*(StirlingS2[n, m] + StirlingS2[n, n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A005589 A052360 A154913 this_sequence A006994 A038627 A155835
Adjacent sequences: A154912 A154913 A154914 this_sequence A154916 A154917 A154918
|
|
KEYWORD
|
nonn,tabf,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 17 2009
|
|
|
Search completed in 0.002 seconds
|
