The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208764 Triangle of coefficients of polynomials v(n,x) jointly generated with A208763; see the Formula section. 3
 1, 0, 3, 0, 2, 7, 0, 2, 6, 19, 0, 2, 6, 26, 47, 0, 2, 6, 34, 78, 123, 0, 2, 6, 42, 110, 258, 311, 0, 2, 6, 50, 142, 426, 758, 803, 0, 2, 6, 58, 174, 626, 1366, 2282, 2047, 0, 2, 6, 66, 206, 858, 2134, 4594, 6558, 5259, 0, 2, 6, 74, 238, 1122, 3062, 7866, 14334 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For a discussion and guide to related arrays, see A208510. As triangle T(n,k) with 0<=k<=n, it is (0, 2/3, 1/3, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (3, -2/3, -4/3, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 02 2012 LINKS FORMULA u(n,x)=u(n-1,x)+2x*v(n-1,x), v(n,x)=2x*u(n-1,x)+x*v(n-1,x), where u(1,x)=1, v(1,x)=1. As triangle T(n,k), 0 <=k<=n : G.f.: (1-x+2y*x)/(1-(1+y)*x -(4*y^2-y)*x^2). - Philippe Deléham, Mar 02 2012 As triangle T(n,k), 0<=k<=n : T(n,k) = T(n-1,k) + T(n-1,k-1) + 4*T(n-2,k-2) - T(n-2,k-1) with T(0,0) = 1, T(1,0) = 0, T(1,1) = 3 and T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 02 2012 EXAMPLE First five rows: 1 0...3 0...2...7 0...2...6...19 0...2...6...26...47 First five polynomials v(n,x): 1 3x 2x + 7x^2 2x + 6x^2 + 19x^3 2x + 6x^2 + 26x^3 + 47x^4 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x]; v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x]; 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[%]    (* A208763 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A208764 *) CROSSREFS Cf. A208763, A208510. Sequence in context: A298058 A298707 A274417 * A209129 A282694 A011075 Adjacent sequences:  A208761 A208762 A208763 * A208765 A208766 A208767 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 02 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 January 22 12:55 EST 2022. Contains 350481 sequences. (Running on oeis4.)