A133038 Cubes of A000931.

1, 0, 0, 1, 0, 1, 1, 1, 8, 8, 27, 64, 125, 343, 729, 1728, 4096, 9261, 21952, 50653, 117649, 274625, 636056, 1481544, 3442951, 8000000, 18609625, 43243551, 100544625, 233744896, 543338496, 1263214441, 2936493568, 6826561273, 15870019697, 36892780289

Offset: 0

Author

Omar E. Pol, Nov 02 2007

Keywords

• easy
• nonn

Examples

			a(10)=27 because Padovan(10)=3 and 3^3=27.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,3,-2,4,-4,-1,-1,0,-1).

Crossrefs

Cf. A000578, A030078, A056570. Padovan sequence: A000931.

Programs

Mathematica

CoefficientList[Series[(1 - x^2)/(1 - x^2 - x^3), {x, 0, 50}], x]^3

Formula

a(n) = A000931(n)^3.

a(n) = a(n-1)+2*a(n-2)+3*a(n-3)-2*a(n-4)+4*a(n-5)-4*a(n-6)-a(n-7)-a(n-8)-a(n-10).

G.f.: (x^9-x^8+x^7+x^6-5*x^5+x^4-2*x^3-2*x^2-x+1) / ((x-1) * (x^3-2*x^2+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