

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
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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

Table of n, a(n) for n=2..20.


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 (getratios seq add?) (cond [(empty? (rest seq)) empty] [else (cons (/ (cond [add? (add1 (first seq))] [else (first seq)]) (second seq)) (getratios (rest seq) add?))])) (define (extendone seq) (local ((define startnext (floor (* (apply max (getratios seq false)) (first seq)))) (define endnext (ceiling (* (apply min (getratios seq true )) (first seq)))) (define ltodo (buildlist ( endnext startnext) (lambda (n) (cons (+ startnext n) seq))))) (cond [(>= (length seq) (sub1 n)) (length ltodo)] [else (apply + (map extendone ltodo))])))) (extendone (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. AdamsWatters, Apr 26 2006


EXTENSIONS

More terms from Joshua Zucker, Jun 05 2006
Comment edited by Franklin T. AdamsWatters, May 14 2010
Ambiguous terms a(0), a(1) removed by Max Alekseyev, Jan 18 2012


STATUS

approved



