A144501 - OEIS

%I #17 Oct 10 2023 05:05:07

%S 1,2,30,1633,198773,42965211,14505751627,7051160946740,

%T 4664901181968498,4030793305701978223,4407914679125170417031,

%U 5950921219972964057360847,9721118017169914469460646225,18898282608956442548700379478918,43117198379072165094561711078882078,114089724623922992953782697056886301761

%N Main diagonal of array in A144502.

%H Seiichi Manyama, <a href="/A144501/b144501.txt">Table of n, a(n) for n = 0..205</a>

%F a(n) ~ 3^(3*n - 3/2) * n^(2*n - 1) / (2^(n-1) * exp(2*n - 1)). - _Vaclav Kotesovec_, Apr 06 2019

%F a(n) = ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8)), with a(0) = 1, a(1) = 2, a(3) = 30. - _G. C. Greubel_, Oct 09 2023

%t a[n_]:= a[n]= If[n==0, 1, If[n<3, 2*(15)^(n-1), (3*(3*n-4)*(3*n-8)*(9*n^2- 21*n+11)*a[n-1] +3*(3*n-2)*a[n-2] -(3*n-5)*(3*n-2)*a[n-3])/(2*(3*n-5)*(3*n-8))]];

%t Table[a[n], {n,0,30}] (* _G. C. Greubel_, Oct 09 2023 *)

%o (Magma) I:=[1,2,30]; [n le 3 select I[n] else ( 3*(3*n-7)*(3*n-11)*(9*n^2 - 39*n + 41)*Self(n-1) + 3*(3*n-5)*Self(n-2) - (3*n-8)*(3*n-5)*Self(n-3) )/(2*(3*n-8)*(3*n-11)): n in [1..30]]; // _G. C. Greubel_, Oct 09 2023

%o (SageMath)

%o @CachedFunction

%o def a(n): # A144503

%o     if (n<3): return (1,2,30)[n]

%o     else: return ( 3*(3*n-4)*(3*n-8)*(9*n^2 - 21*n + 11)*a(n-1) + 3*(3*n-2)*a(n-2) - (3*n-5)*(3*n-2)*a(n-3) )/(2*(3*n-5)*(3*n-8))

%o [a(n) for n in range(31)] # _G. C. Greubel_, Oct 09 2023

%Y Cf. A144502.

%K nonn

%O 0,2

%A _David Applegate_ and _N. J. A. Sloane_, Dec 13 2008