This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209765 Triangle of coefficients of polynomials u(n,x) jointly generated with A209766; see the Formula section. 3
 1, 1, 2, 1, 5, 5, 1, 5, 15, 12, 1, 5, 21, 45, 29, 1, 5, 21, 77, 129, 70, 1, 5, 21, 89, 265, 361, 169, 1, 5, 21, 89, 353, 865, 991, 408, 1, 5, 21, 89, 377, 1325, 2717, 2681, 985, 1, 5, 21, 89, 377, 1549, 4733, 8281, 7169, 2378, 1, 5, 21, 89, 377, 1597, 6125 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Limiting row: F(2+3k), where F=A000045 (Fibonacci numbers) Coefficient of x^n in u(n,x): 1,2,5,12,.... A000129(n) Row sums:  1,3,11,33,101,303,911,2733,..... A081250 Alternating row sums: 1,-1,1,-1,1,-1,,..... A033999 For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x), v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...2 1...5...5 1...5...15...12 1...5...21...45...29 First three polynomials u(n,x): 1, 1 + 2x, 1 + 5x + 5x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x]; v[n_, x_] := 2 x*u[n - 1, x] + 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[%]    (* A209765 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209766 *) Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A081250 *) Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A060925 *) Table[u[n, x] /. x -> -1, {n, 1, z}] (* A033999 *) Table[v[n, x] /. x -> -1, {n, 1, z}] (* A042963 signed *) CROSSREFS Cf. A209766, A208510. Sequence in context: A005605 A300661 A145882 * A209759 A111785 A304462 Adjacent sequences:  A209762 A209763 A209764 * A209766 A209767 A209768 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 14 2012 STATUS approved

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 October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)