cp's OEIS Frontend

A376317 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 4) > 0].

%I A376317 #21 Sep 23 2024 03:49:21
%S A376317 1,2,6,23,100,466,2270,11413,58776,308473,1643922,8872220,48393710,
%T A376317 266357916,1477471248,8251090171,46353709956,261783417427,
%U A376317 1485374891782,8463626764923,48408809202918,277834282516061,1599585546691518,9235769089804804,53466364700486982
%N A376317 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 4) > 0].
%C A376317 Conjecture: cases f(n) = n mod 2 and f(n) = [(n mod 3) > 0] both gives A006318.
%H A376317 Vaclav Kotesovec, <a href="/A376317/b376317.txt">Table of n, a(n) for n = 0..1000</a>
%F A376317 Conjecture: a(n+2) = a(n) + A215973(n+2) - A215973(n+1) (noticed by advanced OEIS search).
%F A376317 Recurrence: (n+1)*a(n) = 4*(2*n-1)*a(n-1) - (11*n-25)*a(n-2) - 2*(2*n+5)*a(n-3) + 12*(n-2)*a(n-4) - 2*(2*n-7)*a(n-5). - _Vaclav Kotesovec_, Sep 23 2024
%o A376317 (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)%4)>0)] + v1[j-1]); v2[i+1] = v1[i+1]); v2
%Y A376317 Cf. A006318, A376388.
%K A376317 nonn
%O A376317 0,2
%A A376317 _Mikhail Kurkov_, Sep 22 2024