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 A079216 Square array A(n>=0,k>=1) (listed antidiagonally: A(0,1)=1, A(1,1)=1, A(0,2)=1, A(2,1)=2, A(1,2)=1, A(0,3)=1, A(3,1)=3, ...) giving the number of n-edge general plane trees fixed by k-fold application of Catalan Automorphisms A057511/A057512 (Deep rotation of general parenthesizations/plane trees). 14
 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 5, 2, 1, 1, 6, 11, 3, 2, 1, 1, 10, 26, 8, 5, 2, 1, 1, 11, 66, 18, 11, 3, 2, 1, 1, 18, 161, 43, 30, 5, 5, 2, 1, 1, 21, 420, 104, 82, 6, 14, 3, 2, 1, 1, 34, 1093, 273, 233, 15, 38, 5, 5, 2, 1, 1, 35, 2916, 702, 680, 36, 111, 6, 11, 3, 2, 1, 1, 68, 7819, 1870 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Note: the counts given here are inclusive, e.g. A(n,6) includes the counts A(n,3) and A(n,2) which in turn both include A(n,1). LINKS A. Karttunen, Catalan Automorphisms FORMULA A(0, k) = 1. A(n, k) = Sum_{r=1..n where r/gcd(r, k) divides n} Sum_{c as each composition of n/(r/gcd(r, k)) into gcd(r, k) parts} Product_{i as each composant of c} A(i-1, lcm(r, k)) MAPLE with(combinat, composition); # composition(n, k) gives ordered partitions of integer n into k parts. [seq(A079216(n), n=0..119)]; A079216 := n -> A079216bi(A025581(n), A002262(n)+1); A079216bi := proc(n, k) option remember; local r; if(0 = n) then RETURN(1); else RETURN(add(PFixedByA057511(n, k, r), r=1..n)); fi; end; PFixedByA057511 := proc(n, k, r) option remember; local ncycles, cyclen, i, c; ncycles := igcd(r, k); cyclen := r/ncycles; if(0 <> (n mod cyclen)) then RETURN(0); else add(mul(A079216bi(i-1, ilcm(r, k)), i=c), c=composition(n/cyclen, ncycles)); fi; end; CROSSREFS A(n, A003418(n)) = A000108(n). The first row: A057546, second: A079223, third: A079224, fourth: A079225, fifth: A079226, sixth: A079227. Cf. also A079217-A079222. Sequence in context: A168396 A049286 A308477 * A181654 A323756 A192710 Adjacent sequences:  A079213 A079214 A079215 * A079217 A079218 A079219 KEYWORD nonn,tabl AUTHOR Antti Karttunen Jan 03 2002 STATUS approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)