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Search: id:A146964
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| A146964 |
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a(n) = ((4+sqrt(7))^n+(4-sqrt(7))^n))/2. |
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+0
2
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| 1, 4, 23, 148, 977, 6484, 43079, 286276, 1902497, 12643492, 84025463, 558412276, 3711069041, 24662841844, 163903113383, 1089259330468, 7238946623297, 48108239012164, 319715392487639, 2124748988791636, 14120553377944337
(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 A146963. Inverse binomial transform of A146965.
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FORMULA
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a(n) = 8*a(n-1)-9*a(n-2); a(0)=1, a(1)=4. G.f.: (1-4*x)/(1-8*x+9*x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr) and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
a(n) = (Sum_{k, 0<=k<=n}A098158(n,k)*4^(2*k)*7^(n-k)}/4^n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 06 2008]
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((4+r7)^n+(4-r7)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008]
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CROSSREFS
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Cf. A146963, A146965, A098158.
Sequence in context: A091642 A162561 A020079 this_sequence A116881 A107089 A055723
Adjacent sequences: A146961 A146962 A146963 this_sequence A146965 A146966 A146967
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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), Nov 03 2008
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 05 2008
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 16 2009
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