This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A208524 Triangle of coefficients of polynomials u(n,x) jointly generated with A208525; see the Formula section. 3
 1, 1, 1, 1, 3, 3, 1, 6, 10, 5, 1, 10, 22, 23, 11, 1, 15, 40, 65, 60, 21, 1, 21, 65, 145, 195, 137, 43, 1, 28, 98, 280, 490, 518, 322, 85, 1, 36, 140, 490, 1050, 1484, 1372, 723, 171, 1, 45, 192, 798, 2016, 3570, 4368, 3447, 1624, 341, 1, 55, 255, 1230, 3570 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Alternating row sums: 1,0,1,0,1,0,1,0,... LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1...1 1...3....3 1...6....10...5 1...10...22...23...11 First five polynomials u(n,x): 1 1 + x 1 + 3x + 3x^2 1 + 6x + 10x^2 + 5x^3 1 + 10x + 22x^2 + 23x^3 + 11x^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_] := 2 x*u[n - 1, x] + (x + 1)*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[%]  (* A208524 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A208525 *) Table[u[n, x] /. x -> 1, {n, 1, z}] (*A060816*) Table[v[n, x] /. x -> 1, {n, 1, z}] (*|A084244|*) Table[u[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*) Table[v[n, x] /. x -> -1, {n, 1, z}](*alt. row sums*) CROSSREFS Cf. A208525. Sequence in context: A110640 A143389 A219218 * A094040 A039798 A193560 Adjacent sequences:  A208521 A208522 A208523 * A208525 A208526 A208527 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 October 15 19:25 EDT 2019. Contains 328037 sequences. (Running on oeis4.)