A153312 Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]); Row sums approximate 2*3^n.

2, 3, 3, 2, 14, 2, 2, 25, 25, 2, 2, 36, 86, 36, 2, 2, 47, 140, 140, 47, 2, 2, 76, 241, 334, 241, 76, 2, 2, 159, 479, 737, 737, 479, 159, 2, 2, 404, 1124, 1702, 1960, 1702, 1124, 404, 2, 2, 1135, 2986, 4284, 5120, 5120, 4284, 2986, 1135, 2, 2, 3324, 8495, 11644, 13778

Offset

0,1

Comments

Row sums:

{2, 6, 18, 54, 162, 378, 972, 2754, 8424, 27054, 89100,...}.

Links

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

Formula

p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]).

Example

{2},
{3, 3},
{2, 14, 2},
{2, 25, 25, 2},
{2, 36, 77, 45, 2},
{2, 65, 167, 176, 74, 2},
{2, 148, 313, 424, 412, 157, 2},
{2, 393, 704, 980, 1079, 812, 402, 2},
{2, 1124, 1826, 1684, 2788, 2620, 1943, 1133, 2},
{2, 3313, 5137, 3510, 6659, 7595, 4563, 5263, 3322, 2},
{2, 9876, 15011, 8647, 10169, 20815, 18719, 9826, 15146, 9885, 2}

Mathematica

Clear[p, n, m, x];
p[x, 3] = 2*x^3 + 25*x^2 + 25*x + 2;
p[x, 4] = 2*x^4 + 36*x^3 + 86*x^2 + 36*x + 2;
p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 3)*Sum[x^i, {i, 1, n - 2}]);
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A153290 A153516 A153311 * A153283 A153288 A153479

Adjacent sequences: A153309 A153310 A153311 * A153313 A153314 A153315

Keyword

nonn,uned,tabl

Author

Roger L. Bagula, Dec 23 2008

Status

approved