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

Author

Omar E. Pol, Nov 02 2007

Keywords

• easy
• nonn

Examples

			a(10)=18 because Padovan(10)=3 and 3^3=27 and 3^2=9 and 27-9=18.
		

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).

Crossrefs

Cf. A000290, A000578, A045991. Padovan sequence: A000931.

Programs

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 *)

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

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

Extensions

Incorrect initial zero of the sequence deleted by Colin Barker, Sep 18 2013

Added more terms, Joerg Arndt, Sep 18 2013