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A068293
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a(1) = 1; thereafter a(n) = 6*(2^(n-1)-1).
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3
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1, 6, 18, 42, 90, 186, 378, 762, 1530, 3066, 6138, 12282, 24570, 49146, 98298, 196602, 393210, 786426, 1572858, 3145722, 6291450, 12582906, 25165818, 50331642, 100663290, 201326586, 402653178, 805306362, 1610612730
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 1/4 the number of colorings of an n X n octagonal array with 4 colors.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009: (Start)
Equals inverse binomial transform of A091344: (1, 7, 31, 115, 391,...)
and binomial transform of (1, 5, 7, 5, 7, 5,...). (End)
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LINKS
| Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
| G.f.: (1+x)*(1+2*x)/((1-x)*(1-2*x)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2002
a(1)=1, a(2)=6, a(3)=18, a(n)=3*a(n-1)-2*a(n-2) [From Harvey P. Dale, Nov 27 2011]
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MATHEMATICA
| a=0; lst={1}; k=6; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 16 2008]
Transpose[NestList[{First[#]+1, 6(2^First[#]-1)}&, {1, 1}, 30]][[2]] (* or *) Join[{1}, LinearRecurrence[{3, -2}, {6, 18}, 30]] (* From Harvey P. Dale, Nov 27 2011 *)
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PROG
| (PARI) a(n)=polcoeff(prod(i=1, 2, (1+i*x))/(prod(i=1, 2, (1-i*x))+x*O(x^n)), n) for(n=0, 50, print1(a(n), ", "))
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CROSSREFS
| Cf. A068239-A068305, A000332, A002417, A027441.
Cf. A091344 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2009]
Sequence in context: A015942 A009945 A011930 * A191101 A184630 A009957
Adjacent sequences: A068290 A068291 A068292 * A068294 A068295 A068296
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Feb 24 2002
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2002
Replaced old definition (which is now a comment) by explicit formula. - N. J. A. Sloane, May 12 2010.
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