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 A209704 Triangle of coefficients of polynomials v(n,x) jointly generated with A209703; see the Formula section. 3
 1, 3, 1, 4, 3, 2, 5, 6, 8, 3, 6, 10, 18, 14, 5, 7, 15, 33, 38, 27, 8, 8, 21, 54, 81, 83, 49, 13, 9, 28, 82, 150, 197, 170, 89, 21, 10, 36, 118, 253, 401, 448, 342, 159, 34, 11, 45, 163, 399, 736, 999, 987, 671, 282, 55, 12, 55, 218, 598, 1253, 1988, 2387, 2106 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n>1, row n starts with n+1, followed by the n-th triangular number, and ends in F(n+1), where F=A000045 (Fibonacci numbers). Column 3: A166830. Row sums: A048654. Alternating row sums: 1,2,3,4,5,6,7,8,9,... For a discussion and guide to related arrays, see A208510. LINKS Table of n, a(n) for n=1..63. FORMULA u(n,x)=x*u(n-1,x)+x*v(n-1,x), v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 3...1 4...3....2 5...6....8....3 6...10...18...14...5 First three polynomials v(n,x): 1, 3 + x , 4 + 3x + 2x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := (x + 1)*u[n - 1, 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[%] (* A209703 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A209704 *) CROSSREFS Cf. A209703, A208510. Sequence in context: A104764 A152842 A307280 * A339106 A082909 A335906 Adjacent sequences: A209701 A209702 A209703 * A209705 A209706 A209707 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified August 3 18:06 EDT 2024. Contains 374899 sequences. (Running on oeis4.)