PROG
(MAGMAMagma) I:=[0, 1]; [n le 2 select I[n] else 4*Self(n-1)+3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 19 2012
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Revision History for A015530
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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MATHEMATICA
a[n_]:=(MatrixPower[{{1, 6}, {1, 3}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
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COMMENTS
In general, x/(1 - a*x - b*x^2) has a(n) = sum_Sum_{k=0..floor((n-1)/2)} C(n-k-1,k)*b^k*a^(n-2k-1). - Paul Barry, Apr 23 2005
LINKS
Lucyna Trojnar-Spelina, and Iwona Włoch, <a href="https://doi.org/10.1007/s40995-019-00757-7">On Generalized Pell and Pell-Lucas Numbers</a>, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
FORMULA
a(n) = sum_Sum_{k=0..floor((n-1)/2)} C(n-k-1, k)*3^k*4^(n-2k-1). - Paul Barry, Apr 23 2005
Limit(a(n+k)/a(k), k=infinity) = A108851(n)+a(n)*sqrt(7).
Limit(A108851(n)/a(n), n=infinity) = sqrt(7). (End)
(End)
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PROG
(Sage) [lucas_number1(n, 4, -3) for n in xrangerange(0, 23)]# Zerinvary Lajos, Apr 23 2009
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