cp's OEIS Frontend

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].

%I A376395 #9 Sep 23 2024 03:49:16
%S A376395 1,2,6,23,102,492,2494,13049,69804,379739,2093908,11676674,65742586,
%T A376395 373229312,2134271056,12282634251,71086381856,413492903669,
%U A376395 2416072302880,14174831386633,83468889675398,493156776790271,2922620673535552,17369048521659378,103489903578100662
%N 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].
%C A376395 Conjecture: cases f(n) = n mod 2 and f(n) = [(n mod 3) > 0] both gives A006318.
%H A376395 Vaclav Kotesovec, <a href="/A376395/b376395.txt">Table of n, a(n) for n = 0..1000</a>
%F A376395 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
%o A376395 (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
%Y A376395 Cf. A006318, A376317, A376388.
%K A376395 nonn
%O A376395 0,2
%A A376395 _Mikhail Kurkov_, Sep 22 2024