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Search: id:A090826
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| A090826 |
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Convolution of Catalan and Fibonacci numbers. |
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+0
4
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| 0, 1, 2, 5, 12, 31, 85, 248, 762, 2440, 8064, 27300, 94150, 329462, 1166512, 4170414, 15031771, 54559855, 199236416, 731434971, 2697934577, 9993489968, 37157691565, 138633745173, 518851050388, 1947388942885, 7328186394725
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also (with a(0)=1 instead of 0): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089867/A089868, i.e. the number of n-node binary trees fixed by the corresponding automorphism(s).
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FORMULA
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CONV(A000045, A000108). [Could somebody supply a g.f. or direct recurrence for this sequence?]
G.f.: (1-(1-4x)^(1/2))/(2(1-x-x^2)). The generating function for the convolution of Catalan and Fibonacci numbers is simply the generating functions of the Catalan and Fibonacci numbers multiplied together. - Molly Leonard (maleonard1(AT)stthomas.edu), Aug 04 2006
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PROGRAM
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(MIT Scheme) (define (A090826 n) (convolve A000045 A000108 n))
(define (convolve fun1 fun2 upto_n) (let loop ((i 0) (j upto_n)) (if (> i upto_n) 0 (+ (* (fun1 i) (fun2 j)) (loop (+ i 1) (- j 1))))))
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CROSSREFS
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Cf. Catalan numbers: A000108, Fibonacci numbers: A000045.
Sequence in context: A071359 A014329 A045633 this_sequence A132441 A000840 A039809
Adjacent sequences: A090823 A090824 A090825 this_sequence A090827 A090828 A090829
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KEYWORD
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nonn,easy
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AUTHOR
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Antti Karttunen (His_Firstname.His_Surname(AT)iki.fi), Dec 20 2003
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