A089984 - OEIS

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A089984

1, 1, 1, 1, ... a, b, c, d, ac-bd, ...

1, 1, 1, 1, 0, 1, -1, 1, -1, 0, 1, 1, -1, 1, -2, -1, 3, 5, -1, -2, 7, -3, -13, 97, 200, 2309, -226573, 45538573, -105193879657, -23833987746960404, 1085365814730154781188953, 114173840897460294190477827374165629

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,15

COMMENTS

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

Sequence b(n,p) = a(n) (mod p), p prime, n>4, is a periodic sequence. Letting l(p) denotes the length of the period of b(n,p) is there any rule for l(p) ? - Benoit Cloitre, Nov 19 2003

LINKS

Table of n, a(n) for n=1..32.

FORMULA

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

a(n) is asymptotic (in absolute value) to B^(r^n) where r is the real root of 1+x^2-x^3 and B>1. - Benoit Cloitre, Nov 19 2003

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==a[n-4]a[n-2]- a[n-3] a[n-1]}, a, {n, 40}] (* Harvey P. Dale, Aug 24 2019 *)

PROG

(PARI) a=b=c=d=1; for(n=5, 30, e=b*d-a*c; a=b; b=c; c=d; d=e; print1(e, ", "))

CROSSREFS

Cf. A089983.

Sequence in context: A130466 A239306 A129322 * A284429 A062105 A210563