A376001 - OEIS

%I #7 Sep 11 2024 00:45:58

%S 1,105,1176,4950,5713890

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

%C The first 5 terms are triangular numbers.

%C a(2), ..., a(5) can all be written as a Narayana number in exactly 4 ways.

%C a(6) > 2*10^35 (if it exists).

%e With T(n,k) = A001263(n,k):

%e       105 = T( 7,3) = T( 7, 5) = T(  15,2) = T(  15,  14);

%e      1176 = T( 9,4) = T( 9, 6) = T(  49,2) = T(  49,  48);

%e      4950 = T(11,4) = T(11, 8) = T( 100,2) = T( 100,  99);

%e   5713890 = T(92,3) = T(92,90) = T(3381,2) = T(3381,3380).

%o (Python)

%o from math import isqrt

%o from bisect import insort

%o from itertools import islice

%o def A010054(n):

%o     return isqrt(m:=8*n+1)**2 == m

%o def A376001_generator():

%o     yield 1

%o     nkN_list = [(5, 3, 20)] # List of triples (n, k, A001263(n, k)), sorted by the last element.

%o     while 1:

%o         N0 = nkN_list[0][2]

%o         c = 0

%o         while 1:

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

%o             if N > N0:

%o                 if c >= 3 or A010054(N0): yield N0

%o                 break

%o             central = n==2*k-1

%o             c += 2-central

%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 central:

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

%o def A376001_list(nmax):

%o     return list(islice(A376001_generator(),nmax))

%Y Cf. A000217, A001263, A003015, A374796, A375573, A375999, A376000.

%K nonn,more

%O 1,2

%A _Pontus von Brömssen_, Sep 06 2024