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A133037
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Squares of members of the Padovan sequence A000931.
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1
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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
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OFFSET
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0,9
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LINKS
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Table of n, a(n) for n=0..37.
Index entries for sequences related to linear recurrences with constant coefficients, signature (1,1,1,-1,1,-1).
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FORMULA
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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).
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EXAMPLE
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a(10)=9 because Padovan(10)=3 and 3^2=9.
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MATHEMATICA
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Clear[a];
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, 30}]
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PROG
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(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
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CROSSREFS
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Cf. A000290, A001248, A007598. Padovan sequence: A000931.
Sequence in context: A165996 A098359 A071567 * A061886 A059815 A202670
Adjacent sequences: A133034 A133035 A133036 * A133038 A133039 A133040
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Omar E. Pol, Nov 02 2007
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EXTENSIONS
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Mathematica program by Olivier Gérard, Jul 05 2011
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STATUS
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approved
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