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 A117294 Number of sequences of length n starting with 1,2 which satisfy a recurrence a(k+1) = floor(c*a(k)) for some constant c. 1
 1, 2, 5, 14, 37, 102, 279, 756, 2070, 5609, 15198, 41530, 114049, 315447, 876513, 2446326, 6861432, 19315953, 54556553 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS It appears that a(n+1)/a(n) may be converging slowly to 3, but even that it converges is not obvious. LINKS EXAMPLE a(4) = 5; length 4 sequences are 1,2,4,8; 1,2,4,9; 1,2,5,12; 1,2,5,13; and 1,2,5,14. PROG (define (A117294 n) (local ((define (get-ratios seq add?) (cond [(empty? (rest seq)) empty] [else (cons (/ (cond [add? (add1 (first seq))] [else (first seq)]) (second seq)) (get-ratios (rest seq) add?))])) (define (extend-one seq) (local ((define startnext (floor (* (apply max (get-ratios seq false)) (first seq)))) (define endnext (ceiling (* (apply min (get-ratios seq true )) (first seq)))) (define ltodo (build-list (- endnext startnext) (lambda (n) (cons (+ startnext n) seq))))) (cond [(>= (length seq) (sub1 n)) (length ltodo)] [else (apply + (map extend-one ltodo))])))) (extend-one (list 2 1)))) - Joshua Zucker, Jun 05 2006 CROSSREFS Some (infinite) examples of such sequences: A000079, A007051, A076883, A001519, A024537, A024576, A057960. Sequence in context: A077938 A077987 A143141 * A148306 A148307 A148308 Adjacent sequences:  A117291 A117292 A117293 * A117295 A117296 A117297 KEYWORD more,nonn AUTHOR Franklin T. Adams-Watters, Apr 26 2006 EXTENSIONS More terms from Joshua Zucker, Jun 05 2006 Comment edited by Franklin T. Adams-Watters, May 14 2010 Ambiguous terms a(0), a(1) removed by Max Alekseyev, Jan 18 2012 STATUS approved

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Last modified January 29 10:34 EST 2020. Contains 331337 sequences. (Running on oeis4.)