

A209762


Triangle of coefficients of polynomials v(n,x) jointly generated with A209761; see the Formula section.


3



1, 2, 2, 3, 5, 4, 4, 10, 14, 8, 5, 17, 34, 36, 16, 6, 26, 68, 104, 88, 32, 7, 37, 120, 240, 296, 208, 64, 8, 50, 194, 480, 776, 800, 480, 128, 9, 65, 294, 868, 1736, 2352, 2080, 1088, 256, 10, 82, 424, 1456, 3472, 5824, 6784, 5248, 2432, 512, 11, 101, 588
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Column 1: 1,2,3,4,5,6,7,8,...
Column 2: 1+1, 1+2^2, 1+3^2, 1+4^2,...
Last term in row n: 2^(n1)
Alternating row sums: 1,0,2,0,2,0,2,0,2,0,2,0,...
For a discussion and guide to related arrays, see A208510.


LINKS

Table of n, a(n) for n=1..58.


FORMULA

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


EXAMPLE

First five rows:
1
2...2
3...5....4
4...10...14...8
5...17...34...36...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 5x + 4x^2.


MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n  1, x] + (x + 1)*v[n  1, x];
v[n_, x_] := x*u[n  1, x] + (x + 1)*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[%] (* A209761 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209762 *)


CROSSREFS

Cf. A209761, A208510.
Sequence in context: A210554 A208912 A210212 * A026408 A301790 A301964
Adjacent sequences: A209759 A209760 A209761 * A209763 A209764 A209765


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Mar 14 2012


STATUS

approved



