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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums:

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

LINKS

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

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

A025192

Sequence in context: A153288 A153479 A153489 * A155688 A215490 A153592

Adjacent sequences:  A153307 A153308 A153309 * A153311 A153312 A153313

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 23 2008

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.