A375999 - OEIS

%I #7 Sep 11 2024 00:45:33

%S 1,3,6,10,15,20,21,28,36,45,50,55,66,78,91,105,120,136,153,171,175,

%T 190,196,210,231,253,276,300,325,336,351,378,406,435,465,490,496,528,

%U 540,561,595,630,666,703,741,780,820,825,861,903,946,990,1035,1081,1128

%N Narayana numbers (A001263), sorted, duplicates removed.

%H Pontus von Brömssen, <a href="/A375999/b375999.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from bisect import insort

%o from itertools import islice

%o def A375999_generator():

%o     yield 1

%o     nkN_list = [(3, 2, 3)] # List of triples (n, k, A001263(n, k)), sorted by the last element.

%o     while 1:

%o         N0 = nkN_list[0][2]

%o         yield N0

%o         while 1:

%o             n, k, N = nkN_list[0]

%o             if N > N0: break

%o             del nkN_list[0]

%o             insort(nkN_list, (n+1, k, n*(n+1)*N//((n-k+1)*(n-k+2))), key=lambda x:x[2])

%o             if n == 2*k-1:

%o                 insort(nkN_list, (n+2, k+1, 4*n*(n+2)*N//(k+1)**2), key=lambda x:x[2])

%o def A375999_list(nmax):

%o     return list(islice(A375999_generator(),nmax))

%Y Cf. A001263, A006987, A024412, A376000, A376001.

%K nonn

%O 1,2

%A _Pontus von Brömssen_, Sep 06 2024