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A110273 a(n) = Pell(n)^3 + Pell(n+1)^3. 1
1, 9, 133, 1853, 26117, 367389, 5169809, 72744121, 1023588937, 14402985777, 202665398173, 2851718540021, 40126725007181, 564625868522949, 7944888884612393, 111793070252410993, 1573047872420021137 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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.
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A366017 A097999 A089547 * A082760 A268654 A112426
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 18 2005
STATUS
approved

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Last modified May 26 22:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)