A133037 Squares of members of the Padovan sequence A000931.

1, 0, 0, 1, 0, 1, 1, 1, 4, 4, 9, 16, 25, 49, 81, 144, 256, 441, 784, 1369, 2401, 4225, 7396, 12996, 22801, 40000, 70225, 123201, 216225, 379456, 665856, 1168561, 2050624, 3598609, 6315169, 11082241, 19448100, 34128964, 59892121, 105103504, 184443561, 323676081

Offset

0,9

Links

Table of n, a(n) for n=0..41.

Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,1,-1).

Formula

a(n) = A000931(n)^2.

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6).

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

Example

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

Mathematica

a[0] = a[3] = a[5] = a[6] = 1; a[1] = a[2] = a[4] = 0; a[n_Integer] := a[n] = 2*a[n - 2] + 2*a[n - 3] - a[n - 7]; Table[a[i], {i, 0, 40}] (* Olivier Gérard, Jul 05 2011 *)
Table[RootSum[-1 - # + #^3 &, #^n (5 - 6 # + 4 #^2) &]^2/529, {n, 0,
40}] (* Eric W. Weisstein, Apr 16 2018 *)
LinearRecurrence[{1, 1, 1, -1, 1, -1}, {1, 0, 0, 1, 0, 1}, 40] (* Eric W. Weisstein, Apr 16 2018 *)

Prog

(PARI) Vec(O(x^20)+(1-x-x^2-x^5)/(1-x-x^2-x^3+x^4-x^5+x^6)) \\ Charles R Greathouse IV, Jul 05 2011

Crossrefs

Cf. A000290, A001248, A007598. Padovan sequence: A000931.

Sequence in context: A071567 A304990 A263727 * A061886 A059815 A202670

Adjacent sequences: A133034 A133035 A133036 * A133038 A133039 A133040

Keyword

easy,nonn

Author

Omar E. Pol, Nov 02 2007

Status

approved