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

1, 3, 6, 10, 15, 20, 21, 28, 36, 45, 50, 55, 66, 78, 91, 105, 120, 136, 153, 171, 175, 190, 196, 210, 231, 253, 276, 300, 325, 336, 351, 378, 406, 435, 465, 490, 496, 528, 540, 561, 595, 630, 666, 703, 741, 780, 820, 825, 861, 903, 946, 990, 1035, 1081, 1128

Offset: 1

Author

Pontus von Brömssen, Sep 06 2024

Keywords

• nonn

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Python

from bisect import insort
from itertools import islice
def A375999_generator():
    yield 1
    nkN_list = [(3, 2, 3)] # List of triples (n, k, A001263(n, k)), sorted by the last element.
    while 1:
        N0 = nkN_list[0][2]
        yield N0
        while 1:
            n, k, N = nkN_list[0]
            if N > N0: break
            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 n == 2*k-1:
                insort(nkN_list, (n+2, k+1, 4*n*(n+2)*N//(k+1)**2), key=lambda x:x[2])
def A375999_list(nmax):
    return list(islice(A375999_generator(),nmax))