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A110273
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a(n) = Pell(n)^3 + Pell(n+1)^3.
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1
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1, 9, 133, 1853, 26117, 367389, 5169809, 72744121, 1023588937, 14402985777, 202665398173, 2851718540021, 40126725007181, 564625868522949, 7944888884612393, 111793070252410993, 1573047872420021137
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..850
Index entries for linear recurrences with constant coefficients, signature (12,30,-12,-1).
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FORMULA
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G.f.: (1+x)*(1-4*x-x^2)/((1+2*x-x^2)*(1-14*x-x^2)).
a(n) = 12*a(n-1) + 30*a(n-2) - 12*a(n-3) - a(n-4).
a(n) = ( 3*(-1)^n*A001333(n) + (Pell(3*n) + Pell(3*(n+1)) )/8.
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MATHEMATICA
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LinearRecurrence[{12, 30, -12, -1}, {1, 9, 133, 1853}, 30] (* Harvey P. Dale, Jan 24 2018 *)
Sum[Fibonacci[Range[0, 30] +j, 2]^3, {j, 0, 1}] (* G. C. Greubel, Sep 17 2021 *)
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PROG
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(Magma) I:=[1, 9, 133, 1853]; [n le 4 select I[n] else 12*Self(n-1) + 30*Self(n-2) - 12*Self(n-3) - Self(n-4): n in [1..31]]; // G. C. Greubel, Sep 17 2021
(Sage) [lucas_number1(n+1, 2, -1)^3 + lucas_number1(n, 2, -1)^3 for n in (0..30)] # G. C. Greubel, Sep 17 2021
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CROSSREFS
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Cf. A000129, A110272.
Sequence in context: A167253 A097999 A089547 * A082760 A268654 A112426
Adjacent sequences: A110270 A110271 A110272 * A110274 A110275 A110276
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jul 18 2005
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STATUS
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approved
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