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 A210871 Triangle of coefficients of polynomials v(n,x) jointly generated with A210870; see the Formula section. 3
 1, 1, 2, 1, 1, 3, 1, 3, 2, 5, 1, 2, 7, 3, 8, 1, 4, 5, 15, 5, 13, 1, 3, 12, 10, 30, 8, 21, 1, 5, 9, 31, 20, 58, 13, 34, 1, 4, 18, 22, 73, 38, 109, 21, 55, 1, 6, 14, 54, 51, 162, 71, 201, 34, 89, 1, 5, 25, 40, 145, 111, 344, 130, 365, 55, 144, 1, 7, 20, 85, 105, 361, 233 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Row n, for n>2, starts with 1 and A028242(n) and ends with F(n-1) and F(n+1), where F=A000045 (Fibonacci numbers). Row sums:  A001045 Alternating row sums: A077925 For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=(x+1)*u(n-1,x)+(x-1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First six rows: 1 1...2 1...1...3 1...3...2....5 1...2...7....3....8 1...4...5....15...5...13 First three polynomials v(n,x): 1, 1 + 2x, 1 + x + 3x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 14; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := (x + 1)*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[%]    (* A210870 *) cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A210871 *) Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A000975 *) Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A001045 *) Table[u[n, x] /. x -> -1, {n, 1, z}] (* A113954 *) Table[v[n, x] /. x -> -1, {n, 1, z}] (* A077925 *) CROSSREFS Cf. A210870, A208510. Sequence in context: A214717 A293312 A136405 * A308399 A287601 A035667 Adjacent sequences:  A210868 A210869 A210870 * A210872 A210873 A210874 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 29 2012 STATUS approved

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