A118330 a(n-1)*a(n-4) + a(n-2)*a(n-5) + a(n-3)*a(n-6), with a(k<6) = 1.

1, 1, 1, 1, 1, 1, 3, 5, 9, 17, 65, 385, 3841, 69087, 4559417, 1759931497, 6761656746177, 467149341275385921, 2129929115299135769778433, 3748529338522222733404780820902657, 25346268690064943238497951432386776919871664547

Offset

0,7

Comments

This is the 3-term analog of the 2-term recurrence A111288 a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-3) + a(n-2)*a(n-4). Primes in this sequence include a(n) for n = 6, 7, 9, ... with a(21) and a(22) composite and the sequence growing beyond my ability to efficiently test primality.

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = 1; for n>5: a(n) = a(n-1)*a(n-4) + a(n-2)*a(n-5) + a(n-3)*a(n-6).

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==1, a[n]== a[n-1] a[n-4]+ a[n-2]a[n-5]+a[n-3]a[n-6]}, a, {n, 30}] (* Harvey P. Dale, Oct 30 2013 *)

Crossrefs

Cf. A111288, A111388.

Sequence in context: A096390 A092264 A135729 * A268212 A062221 A074861

Adjacent sequences: A118327 A118328 A118329 * A118331 A118332 A118333

Keyword

easy,nonn

Author

Jonathan Vos Post, May 14 2006

Extensions

One additional term (a(20)) from Harvey P. Dale, Oct 30 2013

Status

approved