cp's OEIS Frontend

A376001 Numbers that can be written as a Narayana number (A001263) in at least 3 ways.

%I A376001 #7 Sep 11 2024 00:45:58
%S A376001 1,105,1176,4950,5713890
%N A376001 Numbers that can be written as a Narayana number (A001263) in at least 3 ways.
%C A376001 The first 5 terms are triangular numbers.
%C A376001 a(2), ..., a(5) can all be written as a Narayana number in exactly 4 ways.
%C A376001 a(6) > 2*10^35 (if it exists).
%e A376001 With T(n,k) = A001263(n,k):
%e A376001       105 = T( 7,3) = T( 7, 5) = T(  15,2) = T(  15,  14);
%e A376001      1176 = T( 9,4) = T( 9, 6) = T(  49,2) = T(  49,  48);
%e A376001      4950 = T(11,4) = T(11, 8) = T( 100,2) = T( 100,  99);
%e A376001   5713890 = T(92,3) = T(92,90) = T(3381,2) = T(3381,3380).
%o A376001 (Python)
%o A376001 from math import isqrt
%o A376001 from bisect import insort
%o A376001 from itertools import islice
%o A376001 def A010054(n):
%o A376001     return isqrt(m:=8*n+1)**2 == m
%o A376001 def A376001_generator():
%o A376001     yield 1
%o A376001     nkN_list = [(5, 3, 20)] # List of triples (n, k, A001263(n, k)), sorted by the last element.
%o A376001     while 1:
%o A376001         N0 = nkN_list[0][2]
%o A376001         c = 0
%o A376001         while 1:
%o A376001             n, k, N = nkN_list[0]
%o A376001             if N > N0:
%o A376001                 if c >= 3 or A010054(N0): yield N0
%o A376001                 break
%o A376001             central = n==2*k-1
%o A376001             c += 2-central
%o A376001             del nkN_list[0]
%o A376001             insort(nkN_list, (n+1, k, n*(n+1)*N//((n-k+1)*(n-k+2))), key=lambda x:x[2])
%o A376001             if central:
%o A376001                 insort(nkN_list, (n+2, k+1, 4*n*(n+2)*N//(k+1)**2), key=lambda x:x[2])
%o A376001 def A376001_list(nmax):
%o A376001     return list(islice(A376001_generator(),nmax))
%Y A376001 Cf. A000217, A001263, A003015, A374796, A375573, A375999, A376000.
%K A376001 nonn,more
%O A376001 1,2
%A A376001 _Pontus von Brömssen_, Sep 06 2024