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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208608 Triangle of coefficients of polynomials u(n,x) jointly generated with A208609; see the Formula section. 3
 1, 1, 1, 1, 3, 2, 1, 5, 6, 3, 1, 7, 12, 12, 5, 1, 9, 20, 29, 23, 8, 1, 11, 30, 56, 64, 43, 13, 1, 13, 42, 95, 140, 136, 79, 21, 1, 15, 56, 148, 265, 332, 279, 143, 34, 1, 17, 72, 217, 455, 692, 751, 558, 256, 55, 1, 19, 90, 304, 728, 1295, 1708, 1641, 1093, 454 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS coefficient of x^(n-1)=Fibonacci(n)=A000045(n) LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=(x+1)*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...1 1...3...2 1...5...6....3 1...7...12...12...5 First five polynomials u(n,x): 1 1 + x 1 + 3x + 2x^2 1 + 5x + 6x^2 + 3x^3 1 + 7x + 12x^2 + 12x^3 + 5x^4 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := (x + 1)*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[%]  (* A208608 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A208609 *) CROSSREFS Cf. A208609. Sequence in context: A132969 A132970 A192022 * A209577 A139377 A138483 Adjacent sequences:  A208605 A208606 A208607 * A208609 A208610 A208611 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Feb 29 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 July 30 09:18 EDT 2021. Contains 346359 sequences. (Running on oeis4.)