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 A210236 Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section. 4

%I #4 Mar 30 2012 18:58:16

%S 1,3,2,6,8,3,11,22,16,4,19,52,57,28,5,32,112,166,124,45,6,53,228,428,

%T 432,241,68,7,87,446,1018,1300,984,432,98,8,142,848,2285,3540,3397,

%U 2036,728,136,9,231,1578,4912,8964,10443,7962,3914,1168,183,10

%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section.

%C Row sums: powers of 3

%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,...

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

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

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

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

%e First five rows:

%e 1

%e 3....2

%e 6....8....3

%e 11...22...16...4

%e 19...52...57...28...5

%e First three polynomials v(n,x): 1, 3 + 2x , 6 + 8x + 3x^2.

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

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

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

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%] (* A210235 *)

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

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

%t TableForm[cv]

%t Flatten[%] (* A210236 *)

%Y Cf. A210235, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 20 2012

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Last modified July 23 04:24 EDT 2024. Contains 374544 sequences. (Running on oeis4.)