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A089983 1, 1, 1, 1, ... a, b, c, d, ab-cd, ... 1
1, 1, 1, 1, 0, 1, 1, -1, 1, 2, -3, 5, 17, -91, 1532, 139497, -213710951, 29812036392235, 6371158648631364574889, -189937213493701003981668660072118562, 1210120120447335073097142485947209203511752911347585124133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Inspired by the formula for the determinant of a 2 X 2 matrix.

Sequence b(n,p) = a(n) (mod p), p prime, is a periodic sequence. Letting l(p) denotes the length of the period of b(n,p) we get l(2)=5, l(3)=11, l(5)=31... Is there any rule for l(p) ? - Benoit Cloitre, Nov 19 2003

LINKS

Table of n, a(n) for n=1..21.

FORMULA

a(1)=a(2)=a(3)=a(4)=1, for n>4 a(n)=a(n-4)*a(n-3)-a(n-2)*a(n-1).

a(n) is asymptotic (in absolute value) to A^(phi^n) where phi=golden ratio and A=1.005384.. (follows same kind of behavior as A000301, A007660) - Benoit Cloitre, Nov 19 2003

PROG

(PARI) a=b=c=d=1; for(n=5, 20, e=a*b-c*d; a=b; b=c; c=d; d=e; print1(e, ", "))

(MAGMA) I:=[1, 1, 1, 1]; [n le 4 select I[n] else -Self(n-1)*Self(n-2)+Self(n-3)*Self(n-4): n in [1..22]]; // Vincenzo Librandi, Mar 30 2014

CROSSREFS

Cf. A089984.

Sequence in context: A082979 A065952 A308316 * A072858 A276629 A218086

Adjacent sequences:  A089980 A089981 A089982 * A089984 A089985 A089986

KEYWORD

sign,easy

AUTHOR

Ray Chandler, following a suggestion of Rainer Rosenthal, Nov 18 2003

STATUS

approved

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Last modified October 26 06:55 EDT 2021. Contains 348257 sequences. (Running on oeis4.)