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%I #19 Nov 30 2023 01:30:01
%S 1,3,23,314,8209,620297,126742987,47301104551,32606721084786,
%T 61958046554226593,334806306946199122193,3416372868727801226636179,
%U 62595441409640805744780870839,2993270782370572835241882188306602,424202695773047673359251734568172738737
%N A (25,-29) Somos-4 sequence.
%C Hankel transform of A188312.
%H G. C. Greubel, <a href="/A188313/b188313.txt">Table of n, a(n) for n = 0..74</a>
%F a(n) = (25*a(n-1)*a(n-3) - 29*a(n-2)^2)/a(n-4), n>=4.
%F a(n) = b(-2*n) = b(2*n+3) = 2*b(n+2)^3*b(n+3) + b(n+1)^2*(b(n+3)*b(n+4) - b(n+2)*b(n+5)) for all n in Z where b(n) = A006720(n). - _Michael Somos_, Feb 28 2022
%e G.f.: 1 + 3*x + 23*x^2 + 314*x^3 + 8209*x^4 + ... - _Michael Somos_, Feb 28 2022
%t Join[{1, 3, 23, 314}, RecurrenceTable[{a[n] == (25*a[n - 1]*a[n - 3] - 29*a[n - 2]^2)/a[n - 4], a[4] == 8209, a[5] == 620297, a[6] == 126742987, a[7] == 47301104551}, a, {n, 4, 25}]] (* _G. C. Greubel_, Aug 14 2018 *)
%t b[ n_] := If[OddQ[n], a[(n-3)/2], a[-n/2]]; a[ n_] := If[-2<=n<=2, {2, 1, 1, 3, 23}[[n+3]], 2*b[n+2]^3*b[n+3] + b[n+1]^2*(b[n+3]*b[n+4] - b[n+2]*b[n+5])]; (* _Michael Somos_, Feb 28 2022 *)
%o (Magma) I:=[8209, 620297, 126742987, 47301104551]; [1, 3, 23, 314] cat [n le 4 select I[n] else (25*Self(n-1)*Self(n-3) - 29*Self(n-2)^2)/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Aug 14 2018
%Y Cf. A006720.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 28 2011
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