A078918 a(n) = (a(n-1) + a(n-3)) * a(n-2) / a(n-4). a(1) = a(2) = a(3) = a(4) = 1.

1, 1, 1, 1, 2, 3, 8, 30, 132, 1400, 23595, 1107260, 198172975, 156753667213, 1316573850509365, 186386043285609148267, 1238266675343181339894414632, 1472345944138437490816316070884292123

Offset

1,5

Links

Table of n, a(n) for n=1..18.

David Gale, Tracking the Automatic Ant, Chapter 1.

Formula

a(n) * a(n-6) = (a(n-1) + a(n-3)) * (a(n-3) + a(n-5)) for all n in Z. - Michael Somos, Dec 25 2013

a(5-n) = a(n) for all n in Z. - Michael Somos, Dec 25 2013

a(n) = 6 * a(n-2) * a(n-3) - (a(n-2) + a(n-3) + a(n-5)) for all n in Z. - Michael Somos, May 30 2022

Mathematica

a[ n_] := a[n] = If[n < 1, a[5 - n], If[n < 5, 1, (a[n - 1] + a[n - 3]) a[n - 2] / a[n - 4]]]; (* Michael Somos, Dec 25 2013 *)
a[ n_] := a[n] = If[n < 1, a[5 - n], If[n < 6, Max[1, n - 3], 6*a[n - 2]*a[n-3] - (a[n - 2] + a[n - 3] + a[n - 5])]]; (* Michael Somos, May 30 2022 *)

Prog

(PARI) {a(n) = if( n<1, n = 5-n); if( n<5, 1, (a(n-1) + a(n-3)) * a(n-2) / a(n-4))}; /* Michael Somos, Dec 25 2013 */
(PARI) {a(n) = if( n<1, n = 5-n); if( n<6, max(1, n-3), 6*a(n-2)*a(n-3) - (a(n-2)+a(n-3)+a(n-5)))}; /* Michael Somos, May 30 2022 */

Crossrefs

Cf. A078919.

Sequence in context: A332030 A188498 A012886 * A054104 A053556 A301737

Adjacent sequences: A078915 A078916 A078917 * A078919 A078920 A078921

Keyword

nonn

Author

Benoit Cloitre, Dec 13 2002

Status

approved