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A133037 Squares of members of the Padovan sequence A000931. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 19:11 EDT 2020. Contains 338009 sequences. (Running on oeis4.)