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Search: id:A083879
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| A083879 |
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a(0)=1, a(1)=4, a(n)=8a(n-1)-14a(n-2), n>=2. |
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+0
3
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| 1, 4, 18, 88, 452, 2384, 12744, 68576, 370192, 2001472, 10829088, 58612096, 317289536, 1717746944, 9299922048, 50350919168, 272608444672, 1475954689024, 7991119286784, 43265588647936, 234249039168512, 1268274072276992
(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 A083878
4th binomial transform of A077957 . Inverse binomial transform of A083880 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]
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FORMULA
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a(n)=2^((n-2)/2)(2sqrt(2)-1)^n+2^((n-2)/2)(2sqrt(2)+1)^n; a(n)=Sum{k=0..n; C(n, 2k)5^(n-2k)2^k }; G.f.: (1-4x)/(1-8x+14x^2); E.g.f.: exp(4x)cosh(x*sqrt(2)).
((4+sqrt2)^n+(4-sqrt2)^n)/2. Offset=0. a(3)=88. - Al Hakanson (hawkuu(AT)gmail.com), Oct 15 2008
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*2^(3*k-n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]
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CROSSREFS
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Cf. A083880.
Sequence in context: A130524 A083325 A050146 this_sequence A081671 A006629 A068764
Adjacent sequences: A083876 A083877 A083878 this_sequence A083880 A083881 A083882
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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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