A153289 A triangular sequence designed with row sums near 3^n: t(n,m)=If[m == 0 || m == n, Floor[3^n/2^n], Floor[(3^n/2^n)*Binomial[n, m]] + 1].

1, 1, 1, 2, 5, 2, 3, 11, 11, 3, 5, 21, 31, 21, 5, 7, 38, 76, 76, 38, 7, 11, 69, 171, 228, 171, 69, 11, 17, 120, 359, 599, 599, 359, 120, 17, 25, 206, 718, 1436, 1795, 1436, 718, 206, 25, 38, 346, 1384, 3230, 4844, 4844, 3230, 1384, 346, 38, 57, 577, 2595, 6920, 12110

Offset

0,4

Comments

Row sums are:

{1, 2, 7, 24, 78, 242, 745, 2248, 6734, 20114, 60081,...}.

Links

Table of n, a(n) for n=0..59.

Formula

t(n,m)=If[m == 0 || m == n, Floor[3^n/2^n], Floor[(3^n/2^n)*Binomial[n, m]] + 1].

Example

{1},
{1, 1},
{2, 5, 2},
{3, 11, 11, 3},
{5, 21, 31, 21, 5},
{7, 38, 76, 76, 38, 7},
{11, 69, 171, 228, 171, 69, 11},
{17, 120, 359, 599, 599, 359, 120, 17},
{25, 206, 718, 1436, 1795, 1436, 718, 206, 25},
{38, 346, 1384, 3230, 4844, 4844, 3230, 1384, 346, 38},
{57, 577, 2595, 6920, 12110, 14532, 12110, 6920, 2595, 577, 57}

Mathematica

Clear[t, n, m]; t[n_, m_] = If[ m == 0 || m == n, Floor[3^n/2^n], Floor[(3^n/2^n)*Binomial[n, m]] + 1];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A197180 A129396 A274602 * A161643 A196982 A197167

Adjacent sequences: A153286 A153287 A153288 * A153290 A153291 A153292

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 23 2008

Status

approved