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
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
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