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 0, 1, 4, 22, 112, 580, 2992, 15448, 79744, 411664, 2125120, 10970464, 56632576, 292353088, 1509207808, 7790949760, 40219045888, 207621882112, 1071801803776, 5532938507776, 28562564853760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) / a(n-1) converges to sqrt(10) + 2 as n approaches infinity; sqrt(10) + 2 can also be written as sqrt(2) * (sqrt(2) + sqrt(5)), 2 * sqrt(2) * Phi - sqrt(2) + 2 and lim_{n->infinity} sqrt(2) * (sqrt(2) + (L(n) / F(n))), where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein, Lucas Number Eric Weisstein, Lucas Sequence Eric Weisstein, Horadam Sequence Eric Weisstein, Fibonacci Number Eric Weisstein, Pell Number Index entries for linear recurrences with constant coefficients, signature (4, 6). FORMULA a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 4, r = 6. a(n) = ((2+sqrt(10))^n - (2-sqrt(10))^n)/(2*sqrt(10)). - Rolf Pleisch, Jul 06 2009 G.f.: x/(1-4*x-6*x^2). - Colin Barker, Jan 10 2012 EXAMPLE a(4) = 112 because a(3) = 22, a(2) = 4, s = 4, r = 6 and (4 * 22) + (6 * 4) = 112. MATHEMATICA Join[{a=0, b=1}, Table[c=4*b+6*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *) LinearRecurrence[{4, 6}, {0, 1}, 30] (* Harvey P. Dale, Jul 20 2016 *) PROG (Sage) [lucas_number1(n, 4, -6) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 23 2009 (PARI) x='x+O('x^30); concat([0], Vec(x/(1-4*x-6*x^2))) \\ G. C. Greubel, Jan 16 2018 (MAGMA) I:=[0, 1]; [n le 2 select I[n] else 4*Self(n-1) + 6*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018 CROSSREFS Cf. A024318, A000032, A000129. Sequence in context: A144047 A077543 A084157 * A192470 A274799 A290591 Adjacent sequences:  A085936 A085937 A085938 * A085940 A085941 A085942 KEYWORD easy,nonn AUTHOR Ross La Haye, Aug 16 2003 STATUS approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)