login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A153310
Coefficient triangle sequence of a polynomial recursion: p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 1)*x); Row sums are 2*3^n.
0
2, 3, 3, 2, 14, 2, 2, 25, 25, 2, 2, 54, 77, 27, 2, 2, 137, 212, 104, 29, 2, 2, 382, 592, 316, 133, 31, 2, 2, 1113, 1703, 908, 449, 164, 33, 2, 2, 3302, 5003, 2611, 1357, 613, 197, 35, 2, 2, 9865, 14866, 7614, 3968, 1970, 810, 232, 37, 2, 2, 29550, 44414, 22480, 11582
OFFSET
0,1
COMMENTS
Row sums:
{2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 39366, 118098,...}.
FORMULA
p(x,n)=(x + 1)*(p(x, n - 1) + 3^(n - 1)*x).
EXAMPLE
{2},
{3, 3},
{2, 14, 2},
{2, 25, 25, 2},
{2, 54, 77, 27, 2},
{2, 137, 212, 104, 29, 2},
{2, 382, 592, 316, 133, 31, 2},
{2, 1113, 1703, 908, 449, 164, 33, 2},
{2, 3302, 5003, 2611, 1357, 613, 197, 35, 2},
{2, 9865, 14866, 7614, 3968, 1970, 810, 232, 37, 2},
{2, 29550, 44414, 22480, 11582, 5938, 2780, 1042, 269, 39, 2}
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 - 1)*x);
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[p[x, n], x], {n, 0, 10}];
Flatten[%]
CROSSREFS
KEYWORD
nonn,uned,tabl
AUTHOR
Roger L. Bagula, Dec 23 2008
STATUS
approved