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A209565 Triangle of coefficients of polynomials u(n,x) jointly generated with A209566; see the Formula section. 3
1, 1, 1, 1, 4, 1, 1, 4, 11, 1, 1, 4, 14, 26, 1, 1, 4, 14, 45, 57, 1, 1, 4, 14, 48, 133, 120, 1, 1, 4, 14, 48, 161, 366, 247, 1, 1, 4, 14, 48, 164, 520, 952, 502, 1, 1, 4, 14, 48, 164, 557, 1604, 2371, 1013, 1, 1, 4, 14, 48, 164, 560, 1863, 4724, 5711, 2036, 1, 1, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

For a discussion and guide to related arrays, see A208510.

LINKS

Table of n, a(n) for n=1..68.

FORMULA

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

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

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

EXAMPLE

First five rows:

1

1...1

1...4....1

1...4....11...1

1...4...14...26...1

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

MATHEMATICA

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

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

v[n_, x_] := 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[%]   (* A209565 *)

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

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

TableForm[cv]

Flatten[%]   (* A209566 *)

CROSSREFS

Cf. A209566, A208510.

Sequence in context: A124258 A001638 A133826 * A122185 A193752 A136680

Adjacent sequences:  A209562 A209563 A209564 * A209566 A209567 A209568

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 10 2012

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)