A247382 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.

-3, 7, 1, 46, -107, 287, 1753, -2287, 34854, 231113, -994499, -8198929, -82742507, 646912018, 12217516729, 72254901151, 1239086834889, 31471566933049, 60457357235782, 14744625259648249, 371548914696565093, 7621699930737956423, -424588302658797056471

Offset

0,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..150

Formula

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

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.

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

Mathematica

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 *)

Prog

(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)))};
(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]};
(Haskell)
a247382 n = a247382_list !! n
a247382_list = [-3, 7, 1, 46] ++ zipWith (flip div) a247382_list
   (zipWith (+)
        (zipWith (*) (tail a247382_list) (drop 3 a247382_list))
        (zipWith (*) (cycle [-1, 1]) (map (^ 2) $ drop 2 a247382_list)))
-- Reinhard Zumkeller, Sep 17 2014
(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
(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

Crossrefs

Cf. A247378.

Sequence in context: A110238 A077505 A309376 * A031436 A144556 A001439

Adjacent sequences: A247379 A247380 A247381 * A247383 A247384 A247385

Keyword

sign

Author

Michael Somos, Sep 15 2014

Status

approved