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A136433
a(n+2) = a(n+1)*(n mod 3 + 1) + (n mod 2 + 1), a(1) = 11.
0
11, 12, 26, 79, 81, 163, 491, 492, 986, 2959, 2961, 5923, 17771, 17772, 35546, 106639, 106641, 213283, 639851, 639852, 1279706, 3839119, 3839121, 7678243, 23034731, 23034732, 46069466, 138208399, 138208401, 276416803, 829250411, 829250412
OFFSET
1,1
COMMENTS
The sequence goes multiply by 1, add 1, multiply by 2, add 2, multiply by 3, add 1, multiply by 1, add 2, multiply by 2, add 1, multiply by 3, add 2 and then the sequence repeats.
LINKS
Brain Teaser of the Week, Grey matters, Jun 10 2001 - Jun 16 2001.
Puzz.com's 1001 Best Puzzles, Series 2
FORMULA
Conjecture: a(n)=6*a(n-3)+a(n-6)-6*a(n-9). [R. J. Mathar, Oct 30 2008]
EXAMPLE
a(2)=12 because we can write 12 = 11 * 1 + 1.
a(3)=26 because we can write 26 = 12 * 2 + 2.
a(4)=79 because we can write 79 = 26 * 3 + 1.
a(5)=81 because we can write 81 = 79 * 1 + 2.
a(6)=163 because we can write 163 = 81 * 2 + 1.
a(7)=491 because we can write 491 = 163 * 3 + 2.
a(8)=492 because we can write 492 = 491 * 1 + 1.
a(9)=986 because we can write 986 = 492 * 2 + 2.
...
MATHEMATICA
RecurrenceTable[{a[1]==11, a[n]==a[n-1](Mod[n-2, 3]+1)+(Mod[n-2, 2]+1)}, a, {n, 40}] (* or *) LinearRecurrence[{0, 0, 6, 0, 0, 1, 0, 0, -6}, {11, 12, 26, 79, 81, 163, 491, 492, 986}, 40] (* Harvey P. Dale, Aug 14 2013 *)
PROG
(PARI) a=11; for(n=0, 50, print1(a, ", "); a = a*(n%3+1)+n%2+1);
CROSSREFS
Sequence in context: A221644 A022316 A368359 * A172173 A061760 A309631
KEYWORD
nonn
AUTHOR
Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2008
STATUS
approved