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 A209571 Triangle of coefficients of polynomials u(n,x) jointly generated with A209572; see the Formula section. 3
 1, 1, 1, 1, 4, 1, 1, 4, 9, 1, 1, 4, 15, 16, 1, 1, 4, 15, 44, 25, 1, 1, 4, 15, 56, 105, 36, 1, 1, 4, 15, 56, 185, 216, 49, 1, 1, 4, 15, 56, 209, 524, 399, 64, 1, 1, 4, 15, 56, 209, 732, 1295, 680, 81, 1, 1, 4, 15, 56, 209, 780, 2303, 2864, 1089, 100, 1, 1, 4, 15, 56 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Penultimate number in row n is (n-1)^2, for n>1. Combinatorial limit of row n satisfies linear recurrence r(n)=4*r(n-1)-r(n-2) with r(1)=1 and r(2)=4. For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=2x*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...4....1 1...4....9....1 1...4....15...16...1 First three polynomials v(n,x): 1, 1 + x, 1 + 4x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x]; v[n_, x_] := 2 x*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[%]   (* A209571 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209572 *) CROSSREFS Cf. A209572, A208510. Sequence in context: A301626 A080061 A246595 * A269845 A124258 A001638 Adjacent sequences:  A209568 A209569 A209570 * A209572 A209573 A209574 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 11 2012 STATUS approved

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Last modified October 18 05:31 EDT 2019. Contains 328146 sequences. (Running on oeis4.)