A283332 - OEIS

%I #26 Apr 24 2021 03:31:46

%S 1,1,1,1,1,1,1,1,1,4,7,31,223,6943,1548511,10751318815,

%T 16648535451082975,178993712437422911994993439,

%U 744995791758846743179449146618806505170999,19049937502453316579424394593659892304405504872785268490952081866996

%N a(n) = (Sum_{j=1..(K-1)/2} a(n-2*j+1)*a(n-2*j))/a(n-K) with a(1),...,a(K)=1, where K=9.

%H Seiichi Manyama, <a href="/A283332/b283332.txt">Table of n, a(n) for n = 1..25</a>

%H Matthew Christopher Russell, <a href="https://www.semanticscholar.org/paper/Using-experimental-mathematics-to-conjecture-and-in-Russell/fdebe20954dacb7ec7a24afe2cf491b951c5a28d">Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences</a>, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.

%t a[n_]:=If[n<10, 1, Sum[a[n - 2j + 1]*a[n - 2j], {j, 4}]/a[n - 9]]; Table[a[n], {n, 1, 20}] (* _Indranil Ghosh_, Mar 18 2017 *)

%o (PARI) a(n)= if(n<10, 1, sum(j=1, 4, a(n - 2*j + 1)*a(n - 2*j))/a(n - 9));

%o for(n=1, 20, print1(a(n), ", ")) \\ _Indranil Ghosh_, Mar 18 2017

%K nonn

%O 1,10

%A _N. J. A. Sloane_, Mar 17 2017

%E More terms from _Seiichi Manyama_, Mar 17 2017