login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 0
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 (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..58.

FORMULA

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

CROSSREFS

A025192

Sequence in context: A184829 A153290 A153516 * A153312 A153283 A153288

Adjacent sequences:  A153308 A153309 A153310 * A153312 A153313 A153314

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 23 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 25 20:26 EDT 2017. Contains 288730 sequences.