0,2

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.

M. Cook and M. Kleber, Tournament sequences and Meeussen sequences, Electronic J. Comb. 7 (2000), #R44.

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]

Cf. A008934, A058222, A147780, A147794.

Sequence in context: A136384 A123373 A132510 this_sequence A136196 A061100 A147803

Adjacent sequences: A058308 A058309 A058310 this_sequence A058312 A058313 A058314

nonn,new

N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000

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