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%I #19 Aug 08 2023 14:13:38
%S 1,2,13,97,901,29186,1647721,93837697,12290566873,4736355079682,
%T 1969233690270421,1126004701770879841,2327721451902521875261,
%U 7371705459667139440634882,24178816113044965430498802193,208545961878958994572139555513857,4688266673793881234527843412398379761
%N A (9,-5) Somos-4 sequence.
%C Hankel transform of A184018.
%H G. C. Greubel, <a href="/A184019/b184019.txt">Table of n, a(n) for n = 0..75</a>
%H Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Barry/barry601.html">On Motzkin-Schröder Paths, Riordan Arrays, and Somos-4 Sequences</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.7.
%F a(n) = (9*a(n-1)*a(n-3) - 5*a(n-2)^2)/a(n-4).
%t a[n_] := a[n] = (9 a[n - 1] a[n - 3] - 5 a[n - 2]^2)/a[n - 4]; a[0] = 1; a[1] = 2; a[2] = 13; a[3] = 97; Array[a, 17, 0]
%t RecurrenceTable[{a[0]==1,a[1]==2,a[2]==13,a[3]==97,a[n]==(9a[n-1]a[n-3]- 5a[n-2]^2)/a[n-4]},a[n],{n,20}] (* _Harvey P. Dale_, Sep 06 2011 *)
%o (Magma) I:=[901, 29186, 1647721, 93837697]; [1, 2, 13, 97] cat [n le 4 select I[n] else (9*Self(n-1)*Self(n-3) - 5*Self(n-2)^2)/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Aug 14 2018
%Y Cf. A184018.
%K nonn
%O 0,2
%A _Paul Barry_, Jan 08 2011
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