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A058311
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Number of nodes at n-th level in tree in which top node is 1; each node k has children labeled k, k+1, ..., (k+1)^2 at next level.
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3
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1, 4, 48, 7918, 463339346, 7134188685100826388, 13246386641449904934758023373599438217628, 643152870463337226096320122089499144560533929707886143570111588898313745804013188842
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Triggered by a comment from Michael Kleber, Dec 08 2009, who said: The algorithm in my paper with Cook lets you compute the equivalent sequence where the children of a node labelled (k) are labelled with all the integers in the interval [p(k),q(k)] where p,q are any polynomials you like (in the paper, p(k)=k+1 and q(k)=2k). For a bunch of p,q the resulting seq is well-known, eg p(k)=1,q(k)=k+1 is the Catalan numbers.
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LINKS
| M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.
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MAPLE
| M:=4;
L[0]:=[1]; a[0]:=1;
for n from 1 to M do
L[n]:=[];
t1:=L[n-1];
tc:=nops(t1);
for i from 1 to tc do
t2:=t1[i];
for j from t2 to (t2+1)^2 do
L[n]:=[op(L[n]), j]; od:
a[n]:=nops(L[n]);
#lprint(n, L[n], a[n]);
od:
od:
[seq(a[n], n=0..M)];
See the reference for a better way to compute this!
p := proc(n, k) option remember; local j ; if n = 1 then k^2+k+2; # (k+1)^2-(k-1) else sum( procname(n-1, j), j=k..(k+1)^2) ; fi; expand(%) ; end: A058311 := proc(n) if n = 0 then 1 ; else subs(k=1, p(n, k)) ; fi; end: for n from 0 do printf("%d, \n", A058311(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 04 2009]
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CROSSREFS
| Cf. A008934, A058222, A147780, A147794.
Sequence in context: A136384 A123373 A132510 * A189347 A198384 A136196
Adjacent sequences: A058308 A058309 A058310 * A058312 A058313 A058314
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000
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EXTENSIONS
| Corrected, with Maple program, by N. J. A. Sloane, May 03 2009. Thanks to Max Alekseyev for pointing out that something was wrong.
Replaced a(4), added three more terms - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 04 2009
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