A214652 a(n) = (a(n-1) + a(n-4))/gcd(a(n-1), a(n-4)) with a(1) = a(2) = a(3) = a(4) = 1.

1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 7, 12, 19, 29, 36, 4, 23, 52, 22, 13, 36, 22, 2, 15, 17, 39, 41, 56, 73, 112, 153, 209, 282, 197, 350, 559, 841, 1038, 694, 1253, 2094, 522, 608, 1861, 3955, 4477, 5085, 6946, 10901, 1398, 2161, 9107, 20008, 10703, 12864, 21971

Offset: 1

Author

Reed Kelly, Jul 24 2012

Keywords

• nonn

Comments

A variation on A214551 with the first and fourth terms being added and divided by the greatest common divisor of the pair of numbers.

Examples

			a(11) = (a(10)+a(7))/gcd(a(10),a(7)) = (10+4)/gcd(10,4) = 7
a(13) = (a(12)+a(9))/gcd(a(13),a(9)) = (12+7)/gcd(12,7) = 19
		

Links

• Reed Kelly, Table of n, a(n) for n = 1..1004

Crossrefs

cf. A003269, A214551

Programs

Mathematica

GCDxy[n_, x_, y_, init_] := Module[{t, a, i}, t = init;
  Do[AppendTo[t, (t[[-x]] + t[[-y]])/GCD[t[[-x]], t[[-y]]]], {n}];
  t]; GCDxy[100, 1, 4, {1, 1, 1, 1}]
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]+a[n-4])/GCD[ a[n-1],a[n-4]]},a,{n,60}] (* Harvey P. Dale, Apr 08 2019 *)

Extensions

Definition corrected by Harvey P. Dale, Apr 08 2019

NAME adapted to offset and b-file. - R. J. Mathar, Jun 19 2021