A247382 - OEIS

%I #16 Sep 08 2022 08:46:09

%S -3,7,1,46,-107,287,1753,-2287,34854,231113,-994499,-8198929,

%T -82742507,646912018,12217516729,72254901151,1239086834889,

%U 31471566933049,60457357235782,14744625259648249,371548914696565093,7621699930737956423,-424588302658797056471

%N a(n) = (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4) with a(0) = -3, a(1) = 7, a(2) = 1, a(3) = 46.

%H Reinhard Zumkeller, <a href="/A247382/b247382.txt">Table of n, a(n) for n = 0..150</a>

%F 0 = a(n) * a(n+4) - a(n+1) * a(n+3) + (-1)^n * a(n+2)^2 for all n in Z.

%F 0 = a(n) * a(n+9) + a(n+1) * a(n+8) + 9 * a(n+3) * a(n+6) + 9 * a(n+4) * a(n+5) for all n in Z.

%F a(-n) = A247378(n) for all n in Z.

%t RecurrenceTable[{a[0]==-3,a[1]==7,a[2]==1,a[3]==46,a[n]==(a[n-1]a[n-3]- (-1)^n a[n-2]^2)/a[n-4]},a,{n,30}] (* _Harvey P. Dale_, Aug 22 2016 *)

%o (PARI) {a(n) = if( n<-4, (a(n+1) * a(n+3) - (-1)^n * a(n+2)^2) / a(n+4), if( n<0, [1, -2, 1, 1][-n], (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4)))};

%o (PARI) {a(n) = my(A); n=-n; A = if( n<1, n = 6-n; [-1, 1, 1, -2], [1, -2, 1, 1]); A = concat(A, vector(max(0, n-4))); for(k=5, n, A[k] = (A[k-1] * A[k-3] - (-1)^k * A[k-2]^2) / A[k-4]); A[n]};

%o (Haskell)

%o a247382 n = a247382_list !! n

%o a247382_list = [-3, 7, 1, 46] ++ zipWith (flip div) a247382_list

%o    (zipWith (+)

%o         (zipWith (*) (tail a247382_list) (drop 3 a247382_list))

%o         (zipWith (*) (cycle [-1, 1]) (map (^ 2) $ drop 2 a247382_list)))

%o -- _Reinhard Zumkeller_, Sep 17 2014

%o (Magma) I:=[-3,7,1,46]; [n le 4 select I[n] else ( Self(n-1)*Self(n-3) + (-1)^n*Self(n-2)^2 )/Self(n-4): n in [1..30]]; // _G. C. Greubel_, Aug 05 2018

%o (GAP) a:=[-3,7,1,46];; for n in [5..25] do a[n]:=(a[n-1]*a[n-3]-(-1)^(n-1)*a[n-2]^2)/a[n-4]; od; a; # _Muniru A Asiru_, Aug 05 2018

%Y Cf. A247378.

%K sign

%O 0,1

%A _Michael Somos_, Sep 15 2014