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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
OFFSET
0,9
LINKS
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
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