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A209764 Triangle of coefficients of polynomials v(n,x) jointly generated with A209763; see the Formula section. 3
1, 2, 2, 3, 4, 4, 4, 8, 14, 8, 5, 14, 32, 34, 16, 6, 22, 62, 96, 86, 32, 7, 32, 108, 218, 280, 202, 64, 8, 44, 174, 432, 718, 760, 470, 128, 9, 58, 264, 778, 1584, 2194, 1992, 1066, 256, 10, 74, 382, 1304, 3142, 5360, 6382, 5048, 2390, 512, 11, 92, 532 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n begins with n and ends with 2^(n-1).

Row sums:  1,4,11,34,101,304,911,2734,... A060925.

Alternating row sums: 1,0,3,2,5,4,7,6,... A060925.

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

v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,

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

EXAMPLE

First five rows:

1

2...2

3...4....4

4...8....14...8

5...14...32...34...16

First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 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_] := 2 x*u[n - 1, 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[%]    (* A209763 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A209764 *)

Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A081250 *)

Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A060925 *)

Table[u[n, x] /. x -> -1, {n, 1, z}] (* A033999 *)

Table[v[n, x] /. x -> -1, {n, 1, z}] (* A004442*)

CROSSREFS

Cf. A209663, A208510.

Sequence in context: A049980 A209698 A141525 * A071475 A112778 A080594

Adjacent sequences:  A209761 A209762 A209763 * A209765 A209766 A209767

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 14 2012

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)