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

1, 105, 1176, 4950, 5713890

Offset: 1

Author

Pontus von Brömssen, Sep 06 2024

Keywords

• nonn
• more

Comments

The first 5 terms are triangular numbers.

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

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

Examples

			With T(n,k) = A001263(n,k):
      105 = T( 7,3) = T( 7, 5) = T(  15,2) = T(  15,  14);
     1176 = T( 9,4) = T( 9, 6) = T(  49,2) = T(  49,  48);
     4950 = T(11,4) = T(11, 8) = T( 100,2) = T( 100,  99);
  5713890 = T(92,3) = T(92,90) = T(3381,2) = T(3381,3380).
		

Crossrefs

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

Programs

Python

from math import isqrt
from bisect import insort
from itertools import islice
def A010054(n):
    return isqrt(m:=8*n+1)**2 == m
def A376001_generator():
    yield 1
    nkN_list = [(5, 3, 20)] # List of triples (n, k, A001263(n, k)), sorted by the last element.
    while 1:
        N0 = nkN_list[0][2]
        c = 0
        while 1:
            n, k, N = nkN_list[0]
            if N > N0:
                if c >= 3 or A010054(N0): yield N0
                break
            central = n==2*k-1
            c += 2-central
            del nkN_list[0]
            insort(nkN_list, (n+1, k, n*(n+1)*N//((n-k+1)*(n-k+2))), key=lambda x:x[2])
            if central:
                insort(nkN_list, (n+2, k+1, 4*n*(n+2)*N//(k+1)**2), key=lambda x:x[2])
def A376001_list(nmax):
    return list(islice(A376001_generator(),nmax))