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A083878
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a(0)=1, a(1)=3, a(n)=6a(n-1)-7a(n-2), n>=2.
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5
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1, 3, 11, 45, 193, 843, 3707, 16341, 72097, 318195, 1404491, 6199581, 27366049, 120799227, 533233019, 2353803525, 10390190017, 45864515427, 202455762443, 893682966669, 3944907462913, 17413664010795, 76867631824379
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A006012. Second binomial transform of A001333.
3th binomial transform of A077957 . Inverse binomial transform of A083879 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]
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FORMULA
| a(n)=((3-sqrt(2))^n+(3+sqrt(2))^n)/2; a(n)=Sum{k=0..n; C(n, 2k)3^(n-2k)2^k }; G.f.: (1-3x)/(1-6x+7x^2); E.g.f.: exp(3x)cosh(x*sqrt(2)).
a(n)=sum{k=0..n, C(n, k)2^((n-k)/2)(1+(-1)^(n-k))3^k/2} - Paul Barry (pbarry(AT)wit.ie), Jan 22 2005
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*3^(2k-n)*2^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 01 2008]
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MATHEMATICA
| f[n_] := Simplify[(3 + Sqrt@2)^n + (3 - Sqrt@2)^n]/2; Array[f, 23, 0] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 31 2010]
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CROSSREFS
| Cf. A083879.
Sequence in context: A083324 A151113 A151114 * A151115 A151116 A151117
Adjacent sequences: A083875 A083876 A083877 * A083879 A083880 A083881
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 08 2003
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