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Search: id:A083881
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| A083881 |
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a(0)=1, a(1)=3, a(n)=6a(n-1)-6a(n-2), n>=2. |
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+0
6
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| 1, 3, 12, 54, 252, 1188, 5616, 26568, 125712, 594864, 2814912, 13320288, 63032256, 298271808, 1411437312, 6678993024, 31605334272, 149558047488, 707716279296, 3348949390848, 15847398669312, 74990695670784, 354859782008832
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A001075.
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FORMULA
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a(n)=((3-sqrt(3))^n+(3+sqrt(3))^n)/2; a(n)=sum{k=0..floor(n/2); C(n, 2k)3^(n-2k)3^k }; G.f.: (1-3x)/(1-6x+6x^2); E.g.f.: exp(3x)cosh(x*sqrt(3)).
a(n) = right and left terms in M^n * [1 1 1] where M = the 3X3 matrix [1 1 1 / 1 4 1 / 1 1 1]. M^n * [1 1 1] = [a(n) A030192(n) a(n)]. E.g. a(3) = 54 since M^3 * [1 1 1] = [54 144 54] = [a(3) A030192(3) a(3)]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 18 2004
a(n) = Sum_{k, 0<=k<=n}3^k*A098158(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2006
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CROSSREFS
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Cf. A083882.
Cf. A030192.
Adjacent sequences: A083878 A083879 A083880 this_sequence A083882 A083883 A083884
Sequence in context: A120983 A124810 A123348 this_sequence A055835 A125188 A054666
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 08 2003
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