

A210036


Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section.


3



1, 2, 2, 4, 4, 4, 7, 10, 8, 8, 12, 20, 24, 16, 16, 20, 40, 52, 56, 32, 32, 33, 76, 116, 128, 128, 64, 64, 54, 142, 240, 312, 304, 288, 128, 128, 88, 260, 488, 688, 800, 704, 640, 256, 256, 143, 470, 964, 1496, 1856, 1984, 1600, 1408, 512, 512, 232, 840
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

For a discussion and guide to related arrays, see A208510.


LINKS

Table of n, a(n) for n=1..57.


FORMULA

u(n,x)=u(n1,x)+v(n1,x)+1,
v(n,x)=u(n1,x)+x*v(n1,x)+1,
where u(1,x)=1, v(1,x)=1.


EXAMPLE

First five rows:
1
2....2
4....4....4
7....10...8....8
12...20...24...16...16
First three polynomials v(n,x): 1, 2 + 2x , 4 + 4x + 4x^2.


MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n  1, x] + v[n  1, x] + 1;
v[n_, x_] := u[n  1, x] + 2 x*v[n  1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A210035 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210036 *)


CROSSREFS

Cf. A210035, A208510.
Sequence in context: A120456 A115383 A219156 * A304230 A305586 A305040
Adjacent sequences: A210033 A210034 A210035 * A210037 A210038 A210039


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Mar 16 2012


STATUS

approved



