A163147
a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
Original entry on oeis.org
1, 12, 124, 1208, 11456, 107232, 997184, 9242368, 85517056, 790574592, 7305293824, 67488831488, 623410712576, 5758241390592, 53185308114944, 491231692423168, 4537090136866816, 41905067449516032, 387038978271084544
Offset: 0
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[ n le 2 select 11*n-10 else 14*Self(n-1)-44*Self(n-2): n in [1..19] ];
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Vec((1-2*x)/(1-14*x+44*x^2) + O(x^30)) \\ Jinyuan Wang, Mar 23 2020
A153882
a(n) = ((6 + sqrt(5))^n - (6 - sqrt(5))^n)/(2*sqrt(5)).
Original entry on oeis.org
1, 12, 113, 984, 8305, 69156, 572417, 4725168, 38957089, 321004860, 2644388561, 21781512072, 179402099473, 1477598319444, 12169714749665, 100231029093216, 825511191878977, 6798972400658028, 55996821859648049, 461193717895377720
Offset: 1
Al Hakanson (hawkuu(AT)gmail.com), Jan 03 2009
- S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.
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Z:= PolynomialRing(Integers()); N:=NumberField(x^2-5); S:=[ ((6+r)^n-(6-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 04 2009
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I:=[1,12]; [n le 2 select I[n] else 12*Self(n-1)-31*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 01 2016
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LinearRecurrence[{12, -31}, {1, 12}, 25] (* or *) Table[((6 + sqrt(5))^n - (6 - sqrt(5))^n)/(2*sqrt(5)) , {n,0,25}] (* G. C. Greubel, Aug 31 2016 *)
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[lucas_number1(n,12,31) for n in range(1, 21)] # Zerinvary Lajos, Apr 27 2009
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