A133039 a(n) = P(n)^3 - P(n)^2 where P(n) = A000931(n).

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

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