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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+sqrt5)/2]*(1+sqrt2) = (1.618...)*(2.414213...) = 3.9062796...= (1 + sqrt2 + sqrt5 + sqrt10)/2; (since with large n, A000204 is approximated by PHI^n & A002203 is approximated by (1+sqrt2)^n, with the fractional part of each becoming negligible as n approaches infinity. Check: a(11)/a(10) = 3231362/827298 = 3.9059226... LINKS 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). 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). - Colin Barker, Oct 15 2013 CROSSREFS Cf. A085292, A000204, A002203. 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 June 19 11:14 EDT 2019. Contains 324219 sequences. (Running on oeis4.)