|
| |
|
|
A185045
|
|
Triangle of coefficients of polynomials u(n,x) jointly generated with A208659; see the Formula section.
|
|
3
|
|
|
|
1, 1, 2, 1, 6, 4, 1, 10, 16, 8, 1, 14, 36, 40, 16, 1, 18, 64, 112, 96, 32, 1, 22, 100, 240, 320, 224, 64, 1, 26, 144, 440, 800, 864, 512, 128, 1, 30, 196, 728, 1680, 2464, 2240, 1152, 256, 1, 34, 256, 1120, 3136, 5824, 7168, 5632, 2560, 512, 1, 38, 324
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Alternating row sums: 1,-1,-1,-1,-1,-1,-1,-1,-1,...
For a discussion and guide to related arrays, see A208510.
|
|
|
LINKS
|
Table of n, a(n) for n=1..58.
|
|
|
FORMULA
|
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1), T(1,0) = T(2,0) = T(3,0) = 1, T(2,1) = 2, T(3,1) = 6, T(3,2) = 4, T(n,k) = 0 if k<0 or if k>=n. - Philippe Deléham, Mar 19 2012
|
|
|
EXAMPLE
|
First five rows:
1
1...2
1...6...4
1...10...16...8
1...14...36...40...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 10x + 16x^2 + 8x^3
1 + 14x + 36x^2 + 40x^3 + 16x^4
|
|
|
MATHEMATICA
|
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
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[%] (* A185045 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208659 *)
|
|
|
CROSSREFS
|
Cf. A208659, A208510.
Sequence in context: A051482 A349573 A208923 * A208913 A208911 A208761
Adjacent sequences: A185042 A185043 A185044 * A185046 A185047 A185048
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Clark Kimberling, Mar 03 2012
|
|
|
STATUS
|
approved
|
| |
|
|
