A376395 a(n) = P(n+1, n+1) where P(n, m) = P(n, m-1) + P(n-1, m + f(m-n)) for n < m with P(n, m) = P(n-1, m) for 0 <= m <= n and P(0, m) = 1 for m >= 0 and where f(n) = [(n mod 6) > 0].

1, 2, 6, 23, 102, 492, 2494, 13049, 69804, 379739, 2093908, 11676674, 65742586, 373229312, 2134271056, 12282634251, 71086381856, 413492903669, 2416072302880, 14174831386633, 83468889675398, 493156776790271, 2922620673535552, 17369048521659378, 103489903578100662

Offset

0,2

Comments

Conjecture: cases f(n) = n mod 2 and f(n) = [(n mod 3) > 0] both gives A006318.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

Recurrence: (n+1)*a(n) = 2*(7*n-2)*a(n-1) - (67*n-101)*a(n-2) + 32*(4*n-11)*a(n-3) - 8*(8*n-37)*a(n-4) - 2*(22*n-71)*a(n-5) + 4*(n-5)*a(n-6). - Vaclav Kotesovec, Sep 23 2024

Prog

(PARI) upto(n) = my(v1); v1 = vector(2*(n+1), i, 1); v2 = vector(n+1, i, 0); v2[1] = 1; for(i=1, n, for(j=i+1, 2*(n+1)-i, v1[j] = v1[j+(((j-i)%6)>0)] + v1[j-1]); v2[i+1] = v1[i+1]); v2

Crossrefs

Cf. A006318, A376317, A376388.

Sequence in context: A370213 A231444 A248900 * A120346 A050389 A098746

Adjacent sequences: A376392 A376393 A376394 * A376396 A376397 A376398

Keyword

nonn

Author

Mikhail Kurkov, Sep 22 2024

Status

approved