OFFSET
0,1
COMMENTS
Row sums:
{2, 6, 18, 54, 162, 378, 972, 2754, 8424, 27054, 89100,...}.
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
KEYWORD
AUTHOR
Roger L. Bagula, Dec 23 2008
STATUS
approved