A342600 a(n) = f(n,n) where f(m,n) = max(m,n) if m < 2 or n < 2; f(m,n) = f(m-1,n-1) + f(m-1,n-2) + f(m-2,n-1) otherwise. Diagonal of A342859.

0, 1, 3, 7, 17, 39, 91, 211, 487, 1123, 2589, 5963, 13725, 31583, 72661, 167131, 384377, 883951, 2032723, 4674299, 10748631, 24716955, 56839003, 130710843, 300603331, 691345931, 1590077703, 3657329539, 8412668791, 19352107787, 44519281727, 102422137915

Offset

0,3

Comments

It appears that a(n+1)/a(n) tends to 2.314....

Links

Table of n, a(n) for n=0..31.

Formula

a(n) = A342859(n, n).

Mathematica

B[m_, n_] := B[m, n] = Which[m < n, B[n, m], n < 2 || m < 2, Max[m, n], True,
  B[m-1, n-1] + B[m-1, n-2] + B[m-2, n-1]]; Table[B[m, m], {m, 1, 55}]

Prog

(PARI) A342600(n) = A342859(n, n); \\ (Also uses code from A342859.) - Antti Karttunen, Mar 28 2021
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A342600(n, m=None): # A342600(n) = A342600(n, n)
    if m == None: m = n
    return max(m, n) if m < 2 or n < 2 else A342600(n-1, m-1)+A342600(n-1, m-2)+A342600(n-2, m-1)
for i in range(32): print(i, A342600(i)) # Chai Wah Wu, Apr 22 2021

Crossrefs

Main diagonal of A342859. Cf. A001850.

Sequence in context: A127984 A157029 A191825 * A229514 A077927 A005197

Adjacent sequences: A342597 A342598 A342599 * A342601 A342602 A342603

Keyword

nonn

Author

José María Grau Ribas, Mar 25 2021

Status

approved