A153311 Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))); Row sums are 2*3^n.

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

Offset: 0

Author

Roger L. Bagula, Dec 23 2008

Keywords

• nonn
• uned
• tabl

Comments

Row sums:

{2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}.

Examples

			{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}
		

Crossrefs

A025192

Programs

Mathematica

Clear[p, n, m, x];
p[x, 0] = 2; p[x, 1] = 3*x + 3; p[x, 2] = 2*x^2 + 14*x + 2;
p[x_, n_] := p[x, n] = (x + 1)*(p[x, n - 1] + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2)));
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]

Formula

p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 2)*(x + x^Floor[n/2] + x^(n - 2))).