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 A085293 Product of Lucas (A000204) and a Pell Companion series (A002203). 1
 2, 18, 56, 238, 902, 3564, 13862, 54238, 211736, 827298, 3231362, 12623044, 49308482, 192613698, 752401496, 2939092798, 11480914982, 44847668844, 175187526662, 684331472398, 2673190054136, 10442227799538, 40790261396162, 159338166024964, 622419427368002 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Convergent a(n+1)/a(n) = ((1+sqrt(5))/2)*(1+sqrt(2)) = (1.618...)*(2.414213...) = 3.9062796... = (1 + sqrt(2) + sqrt(5) + sqrt(10))/2. LINKS Table of n, a(n) for n=1..25. Index entries for linear recurrences with constant coefficients, signature (2,7,2,-1). FORMULA a(n) = A000204(n) * A002203(n), n > 0. a(n) = 2*A085292(n). a(n) = (((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n) * ((1+sqrt(2))^n + (1-sqrt(2))^n). From Colin Barker, Oct 15 2013: (Start) a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) - a(n-4). G.f.: -2*x*(2*x^3 - 3*x^2 - 7*x - 1) / (x^4 - 2*x^3 - 7*x^2 - 2*x + 1). (End) E.g.f.: 4*(exp(x/2)*(cosh(x/sqrt(2))*cosh(sqrt(5/2)*x)*cosh(sqrt(5)*x/2)+sinh(x/sqrt(2))*sinh(sqrt(5/2)*x)*sinh(sqrt(5)*x/2))-1). - Stefano Spezia, Aug 25 2019 PROG (Magma) I:=[2, 18, 56, 238]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) + 2*Self(n-3) - Self(n-4):n in [1..30]]; // Marius A. Burtea, Aug 25 2019 CROSSREFS Cf. A000204, A002203, A085292. Sequence in context: A058653 A058794 A114109 * A119118 A213820 A078837 Adjacent sequences: A085290 A085291 A085292 * A085294 A085295 A085296 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jun 24 2003 EXTENSIONS More terms from David Wasserman, Jan 31 2005 More terms from Colin Barker, Oct 16 2013 STATUS approved

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Last modified September 8 02:36 EDT 2024. Contains 375749 sequences. (Running on oeis4.)