The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A210743 Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section. 3

%I

%S 1,2,3,4,8,7,7,20,25,17,12,43,76,75,41,20,88,194,264,216,99,33,172,

%T 458,770,861,606,239,54,327,1016,2038,2811,2691,1667,577,88,608,2161,

%U 5012,8206,9689,8149,4517,1393,143,1112,4447,11699,22057,30830

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210744; see the Formula section.

%C Row n starts with -1+F(n), where F=A000045 (Fibonacci numbers), and ends with A001333(n). For a discussion and guide to related arrays, see A208510.

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

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

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

%e First five rows:

%e 1

%e 2....3

%e 4....8....7

%e 7....20...25...17

%e 12...43...76...75...41

%e First three polynomials u(n,x): 1, 2+ 3x, 4 + 8x + 7x^2.

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

%t u[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;

%t v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A210743 *)

%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[%] (* A210744 *)

%Y Cf. A210744, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 24 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 26 01:22 EST 2020. Contains 338631 sequences. (Running on oeis4.)