A176388 A symmetrical triangle:t(n,m)=Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/( 2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1]

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 3, 5, 3, 1, 1, 11, 21, 21, 11, 1, 1, 6, 13, 16, 13, 6, 1, 1, 34, 76, 106, 106, 76, 34, 1, 1, 15, 33, 50, 56, 50, 33, 15, 1, 1, 112, 258, 402, 493, 493, 402, 258, 112, 1, 1, 40, 91, 146, 188, 204, 188, 146, 91, 40, 1

Offset

0,5

Comments

The sequence is an approximate adjusted normal probability distribution made integer by the Floor[] operation.

Row sums are:

{1, 2, 4, 10, 13, 66, 56, 434, 254, 2532, 1136,...}.

Links

Table of n, a(n) for n=0..65.

Formula

t(n,m)=Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/( 2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1]

Example

{1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 3, 5, 3, 1},
{1, 11, 21, 21, 11, 1},
{1, 6, 13, 16, 13, 6, 1},
{1, 34, 76, 106, 106, 76, 34, 1},
{1, 15, 33, 50, 56, 50, 33, 15, 1},
{1, 112, 258, 402, 493, 493, 402, 258, 112, 1},
{1, 40, 91, 146, 188, 204, 188, 146, 91, 40, 1}

Mathematica

t0[n_, m_] = Floor[(n!/Floor[n/2]!^2)*(Exp[ -(m - n/2)^2/(2*((n + 1)/4)^2)] - Exp[ -(n/2)^2/(2*((n + 1)/4)^2)]) + 1];
Table[Table[t0[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A350912 A055370 A350021 * A282494 A156609 A026637

Adjacent sequences: A176385 A176386 A176387 * A176389 A176390 A176391

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 16 2010

Status

approved