A207615 Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; see the Formula section.

1, 3, 1, 6, 4, 1, 12, 11, 5, 1, 24, 28, 17, 6, 1, 48, 68, 51, 24, 7, 1, 96, 160, 142, 82, 32, 8, 1, 192, 368, 376, 255, 122, 41, 9, 1, 384, 832, 960, 744, 417, 172, 51, 10, 1, 768, 1856, 2384, 2072, 1323, 639, 233, 62, 11, 1, 1536, 4096, 5792, 5568, 3974

Offset

1,2

Comments

Riordan array ((1 + z)/(1 - 2*z), z*(1 - z)/(1 - 2*z)). - Peter Bala, Dec 31 2015

Links

Table of n, a(n) for n=1..60.

Formula

u(n,x) = u(n-1,x) + v(n-1,x),

v(n,x) = u(n-1,x) + (x + 1)*v(n-1,x) + 1,

where u(1,x) = 1, v(1,x) = 1.

Example

First five rows:
   1
   3  1
   6  4  1
  12 11  5  1
  24 28 17  6  1

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%]    (* A207614 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]    (* A207615 *)

Crossrefs

Cf. A207614, A208510, A003945, A011782.

Sequence in context: A185944 A131415 A210230 * A209165 A121437 A078585

Adjacent sequences: A207612 A207613 A207614 * A207616 A207617 A207618

Keyword

nonn,tabl,easy

Author

Clark Kimberling, Feb 20 2012

Status

approved