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%I #22 Apr 16 2018 15:39:04
%S 1,0,0,1,0,1,1,1,4,4,9,16,25,49,81,144,256,441,784,1369,2401,4225,
%T 7396,12996,22801,40000,70225,123201,216225,379456,665856,1168561,
%U 2050624,3598609,6315169,11082241,19448100,34128964,59892121,105103504,184443561,323676081
%N Squares of members of the Padovan sequence A000931.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,1,-1).
%F a(n) = A000931(n)^2.
%F a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6).
%F G.f.: (x^5+x^2+x-1)/(-x^6+x^5-x^4+x^3+x^2+x-1).
%e a(10)=9 because Padovan(10)=3 and 3^2=9.
%t 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 *)
%t Table[RootSum[-1 - # + #^3 &, #^n (5 - 6 # + 4 #^2) &]^2/529, {n, 0,
%t 40}] (* _Eric W. Weisstein_, Apr 16 2018 *)
%t LinearRecurrence[{1, 1, 1, -1, 1, -1}, {1, 0, 0, 1, 0, 1}, 40] (* _Eric W. Weisstein_, Apr 16 2018 *)
%o (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
%Y Cf. A000290, A001248, A007598. Padovan sequence: A000931.
%K easy,nonn
%O 0,9
%A _Omar E. Pol_, Nov 02 2007
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