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A136433
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a(n+2)=a(n+1)*(n mod 3 + 1) + (n mod 2 + 1), a(1)=11.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Brain Teaser of the Week, Grey matters, Jun 10 2001 - Jun 16 2001.
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FORMULA
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Conjecture: a(n)=6*a(n-3)+a(n-6)-6*a(n-9). [From R. J. Mathar, Oct 30 2008]
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EXAMPLE
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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.
...
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MATHEMATICA
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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 *)
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PROG
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(PARI) a=11; for(n=0, 50, print1(a", "); a=a*(n%3+1)+n%2+1)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 01 2008
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STATUS
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approved
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