A136433 a(n+2) = a(n+1)*(n mod 3 + 1) + (n mod 2 + 1), a(1) = 11.

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

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

Brain Teaser of the Week, Grey matters, Jun 10 2001 - Jun 16 2001.

Puzz.com's 1001 Best Puzzles, Series 2

Rand Personnel, Quick Questions: Series 2

Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,1,0,0,-6).

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

Adjacent sequences: A136430 A136431 A136432 * A136434 A136435 A136436

Keyword

nonn

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2008

Status

approved