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A209165 Triangle of coefficients of polynomials v(n,x) jointly generated with A209164; see the Formula section. 3
1, 3, 1, 6, 4, 1, 12, 14, 7, 1, 24, 40, 28, 8, 1, 48, 104, 96, 44, 11, 1, 96, 256, 296, 184, 66, 12, 1, 192, 608, 848, 664, 316, 90, 15, 1, 384, 1408, 2304, 2176, 1296, 496, 120, 16, 1, 768, 3200, 6016, 6656, 4768, 2288, 736, 152, 19, 1, 1536, 7168, 15232 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 1,2,3,4,5,6,7,8,9,10,11,...

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

v(n,x)=(x+1)*u(n-1,x)+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...14...7....1

24...40...28...8...1

First three polynomials v(n,x): 1, 3 + x, 6 + 4x + x^2.

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];

v[n_, x_] := (x + 1)*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[%]    (* A209164 *)

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

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

TableForm[cv]

Flatten[%]    (* A209165 *)

CROSSREFS

Cf. A209164, A208510.

Sequence in context: A131415 A210230 A207615 * A121437 A078585 A116551

Adjacent sequences:  A209162 A209163 A209164 * A209166 A209167 A209168

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 08 2012

STATUS

approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)