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A209148 Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section. 3
1, 2, 1, 5, 5, 1, 11, 16, 7, 1, 23, 44, 30, 9, 1, 47, 112, 104, 48, 11, 1, 95, 272, 320, 200, 70, 13, 1, 191, 640, 912, 720, 340, 96, 15, 1, 383, 1472, 2464, 2352, 1400, 532, 126, 17, 1, 767, 3328, 6400, 7168, 5152, 2464, 784, 160, 19, 1, 1535, 7424 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Alternating row sums: 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) = u(n-1,x) + (x+1)*v(n-1,x)+1,

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

T(n,k) = 3*T(n-1,k)+T(n-1,k-1)-2*T(n-2,k)-T(n-2,k-1), T(1,0)=T(2,1)=T(3,2)=1, T(2,0)=2, T(3,0)=T(3,1)=5, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Jan 17 2014

EXAMPLE

First five rows:

  1

  2....1

  5....5....1

  11...16...7....1

  23...44...30...9...1

First three polynomials v(n,x): 1, 2 + x, 5 + 5x + 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_] := u[n - 1, x] + (x + 1)*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[%]    (* A209148 *)

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

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

TableForm[cv]

Flatten[%]    (* A209149 *)

CROSSREFS

Cf. A209149, A208510.

Sequence in context: A204111 A079502 A209164 * A126124 A123971 A060920

Adjacent sequences:  A209145 A209146 A209147 * A209149 A209150 A209151

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 07 2012

EXTENSIONS

Example corrected by Philippe Deléham, Jan 17 2014

STATUS

approved

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Last modified December 19 10:10 EST 2018. Contains 318246 sequences. (Running on oeis4.)