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 A133039 a(n) = P(n)^3 - P(n)^2 where P(n) = A000931(n). 1
 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 18, 48, 100, 294, 648, 1584, 3840, 8820, 21168, 49284, 115248, 270400, 628660, 1468548, 3420150, 7960000, 18539400, 43120350, 100328400, 233365440, 542672640, 1262045880, 2934442944, 6822962664, 15863704528, 36881698048, 85746672900, 199347278724, 463445232298 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,2,1,-9,3,-9,3,-3,15,-9,9,-3,1,-2,1,-1). FORMULA a(n) = P(n)^3 - P(n)^2 = A000931(n)^3 - A000931(n)^2. G.f.: 2*x^8*(x^7-x^6+2*x^5+x^2-2*x+2) / ((x-1) * (x^3-2*x^2+3*x-1) * (x^3-x^2+2*x-1) * (x^3-x-1) * (x^6+3*x^5+5*x^4+5*x^3+5*x^2+3*x+1)). - Colin Barker, Sep 18 2013 EXAMPLE a(10)=18 because Padovan(10)=3 and 3^3=27 and 3^2=9 and 27-9=18. MATHEMATICA P[0] := 1; P[1] := 0; P[2] := 0; P[n_] := P[n] = P[n - 2] + P[n - 3]; Table[P[n]^3 - P[n]^2, {n, 0, 50}] (* G. C. Greubel, Oct 02 2017 *) PROG (PARI) x='x+O('x^50); concat([0, 0, 0, 0, 0, 0, 0, 0], Vec(2*x^8*(x^7-x^6+2*x^5+x^2-2*x+2)/((x -1)*(x^3-2*x^2+3*x-1)*(x^3-x^2+2*x-1)*(x^3-x-1)*(x^6+3*x^5+5*x^4 +5*x^3 +5*x^2+3*x+1)))) \\ G. C. Greubel, Oct 02 2017 CROSSREFS Cf. A000290, A000578, A045991. Padovan sequence: A000931. Sequence in context: A214166 A214187 A214238 * A177117 A272321 A272290 Adjacent sequences: A133036 A133037 A133038 * A133040 A133041 A133042 KEYWORD easy,nonn AUTHOR Omar E. Pol, Nov 02 2007 EXTENSIONS Incorrect initial zero of the sequence deleted by Colin Barker, Sep 18 2013 Added more terms, Joerg Arndt, Sep 18 2013 STATUS approved

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Last modified September 7 13:22 EDT 2024. Contains 375730 sequences. (Running on oeis4.)