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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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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A083878
4th binomial transform of A077957 . Inverse binomial transform of A083880 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]
Contribution from L. Edson Jeffery, Apr 26, 2011. (Start):
Let G be the Gram matrix
G=
(4 1 0 1)
(1 4 1 0)
(0 1 4 -1)
(1 0 -1 4)
of A028997. Then a(n)=(1/4)*Trace(G^n). (End)
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FORMULA
| 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
| Cf. A028997, A083880.
Sequence in context: A199309 A083325 A050146 * A081671 A006629 A068764
Adjacent sequences: A083876 A083877 A083878 * A083880 A083881 A083882
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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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