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Search: id:A117294
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| A117294 |
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Number of sequences of length n starting with 1,2 which satisfy a recurrence a(k+1) = floor(c*a(k)). |
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1
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| 1, 1, 1, 2, 5, 14, 37, 102, 279, 756, 2070, 5609, 15198, 41530, 114049, 315447, 876513, 2446326, 6861432, 19315953, 54556553
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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It seems that a(n+1)/a(n) may be converging to something close to 2.7, but even that it converges is not obvious.
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EXAMPLE
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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.
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PROGRAM
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(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 (joshua.zucker(AT)stanfordalumni.org), Jun 05 2006
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CROSSREFS
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Some (infinite) examples of such sequences: A000079, A007051, A076883, A001519, A024537, A024576, A057960.
Sequence in context: A077938 A077987 A143141 this_sequence A148306 A148307 A148308
Adjacent sequences: A117291 A117292 A117293 this_sequence A117295 A117296 A117297
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KEYWORD
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more,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 26 2006
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EXTENSIONS
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More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 05 2006
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