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Search: id:A145303
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| A145303 |
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a(n) = ((8+sqrt(8))^n+(8-sqrt(8))^n)/2. |
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+0
4
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| 1, 8, 72, 704, 7232, 76288, 815616, 8777728, 94769152, 1024753664, 11088986112, 120037572608, 1299617939456, 14071782965248, 152369922834432, 1649898919297024, 17865667030024192, 193456332999753728
(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 is A152267, inverse binomial transform is A147689.
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FORMULA
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a(n) = 16*a(n-1)-56*a(n-2). G.f.: (1-8x)/(1-16x+56x^2). a(n) = 2^n*A081180(n+1)-2^(n+2)*A081180(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008]
a(n) = Sum_{k, 0<=k<=n}8^k*A098158(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 14 2008]
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((8+r8)^n+(8-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 20 2008]
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CROSSREFS
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Cf. A081180, A098158, A152267, A147689.
Sequence in context: A115970 A078995 A082414 this_sequence A098411 A165323 A082366
Adjacent sequences: A145300 A145301 A145302 this_sequence A145304 A145305 A145306
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 09 2009
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