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 A006277 a(n) = (a(n-1) + 1)*a(n-2). (Formerly M0888) 6
 1, 1, 2, 3, 8, 27, 224, 6075, 1361024, 8268226875, 11253255215681024, 93044467205527772332546875, 1047053135870867396062743192203958743681024, 97422501162981936223682742789520433197690551802305989766350860546875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 6.7. Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 6.10 Quadratic recurrence constants, pp. 445-446. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. L. Davison, Jeffrey Shallit, Continued Fractions for Some Alternating Series, Monatsh. Math., 111 (1991), 119-126. FORMULA sum_{n>=0} 1/a(n) = 3. - Gerald McGarvey, Jul 20 2004 a(n) = floor(A243967^(phi^n) * A243968^((1-phi)^n)), where phi is the golden ratio (1+sqrt(5))/2. - Vaclav Kotesovec, Jan 19 2015 MAPLE A006277 := proc(n) options remember; if n <= 1 then RETURN(1) else A006277(n-2)*(A006277(n-1)+1); fi; end; MATHEMATICA a=b=1; lst={a, b}; Do[AppendTo[lst, c=a*b+a]; a=b; b=c, {n, 0, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, May 06 2010 *) RecurrenceTable[{a[n]==a[n-2]*(1+a[n-1]), a[0]==1, a[1]==1}, a, {n, 0, 15}] (* Vaclav Kotesovec, Jan 19 2015 *) PROG (Haskell) a006277_list = 1 : scanl ((*) . (+ 1)) 2 a006277_list -- Jack Willis, Dec 22 2013 (Maxima) a(n) := if (n = 0 or n = 1) then 1 else a(n-2)*(a(n-1)+1) \$ makelist(a(n), n, 0, 12); Emanuele Munarini, Mar 23 2017 (MAGMA) [n le 2 select 1 else (Self(n-1) + 1)*Self(n-2): n in [1..15]]; // Vincenzo Librandi, May 23 2019 CROSSREFS Cf. A243967, A243968. Sequence in context: A093858 A080568 A091339 * A186927 A177010 A300484 Adjacent sequences:  A006274 A006275 A006276 * A006278 A006279 A006280 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladimir Joseph Stephan Orlovsky, May 06 2010 STATUS approved

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Last modified October 18 07:19 EDT 2019. Contains 328146 sequences. (Running on oeis4.)