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

0,9

Links

Table of n, a(n) for n=0..35.

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A077110 A333625 A098360 * A339734 A341834 A255275

Adjacent sequences: A133035 A133036 A133037 * A133039 A133040 A133041

Keyword

easy,nonn

Author

Omar E. Pol, Nov 02 2007

Status

approved