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A209154 Triangle of coefficients of polynomials u(n,x) jointly generated with A209157; see the Formula section. 3
1, 2, 1, 4, 5, 2, 7, 14, 10, 2, 11, 32, 36, 18, 4, 16, 65, 104, 82, 32, 4, 22, 121, 258, 282, 168, 52, 8, 29, 210, 574, 820, 676, 328, 88, 8, 37, 344, 1176, 2116, 2264, 1504, 608, 136, 16, 46, 537, 2256, 4980, 6640, 5672, 3136, 1096, 224, 16, 56, 805 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last number in each row is a power of 2.

Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...

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

LINKS

Table of n, a(n) for n=1..57.

FORMULA

u(n,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....1

4....5....2

7....14...10...2

11...32...36...18...4

First three polynomials v(n,x): 1, 2 + x, 4 + 5x + 2x^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_] := 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[%]    (* A209154 *)

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

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

TableForm[cv]

Flatten[%]    (* A209157 *)

CROSSREFS

Cf. A209157, A208510.

Sequence in context: A145064 A209166 A209146 * A144332 A209153 A209141

Adjacent sequences:  A209151 A209152 A209153 * A209155 A209156 A209157

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

STATUS

approved

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