OFFSET
1,2
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).
EXAMPLE
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).
PROG
(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))
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Sep 06 2024
STATUS
approved