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A375999 Narayana numbers (A001263), sorted, duplicates removed.

%I A375999 #7 Sep 11 2024 00:45:33
%S A375999 1,3,6,10,15,20,21,28,36,45,50,55,66,78,91,105,120,136,153,171,175,
%T A375999 190,196,210,231,253,276,300,325,336,351,378,406,435,465,490,496,528,
%U A375999 540,561,595,630,666,703,741,780,820,825,861,903,946,990,1035,1081,1128
%N A375999 Narayana numbers (A001263), sorted, duplicates removed.
%H A375999 Pontus von Brömssen, <a href="/A375999/b375999.txt">Table of n, a(n) for n = 1..10000</a>
%o A375999 (Python)
%o A375999 from bisect import insort
%o A375999 from itertools import islice
%o A375999 def A375999_generator():
%o A375999     yield 1
%o A375999     nkN_list = [(3, 2, 3)] # List of triples (n, k, A001263(n, k)), sorted by the last element.
%o A375999     while 1:
%o A375999         N0 = nkN_list[0][2]
%o A375999         yield N0
%o A375999         while 1:
%o A375999             n, k, N = nkN_list[0]
%o A375999             if N > N0: break
%o A375999             del nkN_list[0]
%o A375999             insort(nkN_list, (n+1, k, n*(n+1)*N//((n-k+1)*(n-k+2))), key=lambda x:x[2])
%o A375999             if n == 2*k-1:
%o A375999                 insort(nkN_list, (n+2, k+1, 4*n*(n+2)*N//(k+1)**2), key=lambda x:x[2])
%o A375999 def A375999_list(nmax):
%o A375999     return list(islice(A375999_generator(),nmax))
%Y A375999 Cf. A001263, A006987, A024412, A376000, A376001.
%K A375999 nonn
%O A375999 1,2
%A A375999 _Pontus von Brömssen_, Sep 06 2024