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Search: id:A145302
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| A145302 |
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a(n) = ((7+sqrt(7))^n+(7-sqrt(7))^n)/2. |
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+0
4
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| 1, 7, 56, 490, 4508, 42532, 406112, 3899224, 37532432, 361686640, 3487250816, 33630672544, 324364881344, 3128620091968, 30177356271104, 291080943932800, 2807684251672832, 27082179878242048, 261227779725129728
(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 A152265, inverse binomial transform is A146966.
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FORMULA
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a(n) = 14*a(n-1)-42*a(n-2). G.f.: (1-7x)/(1-14x+42x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008]
a(n)=Sum_{k, 0<=k<=n}7^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<r7>:=NumberField(x^2-7); S:=[ ((7+r7)^n+(7-r7)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 20 2008, Jul 09 2009]
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CROSSREFS
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Cf. A098158, A152265, A146966
Sequence in context: A147839 A126694 A024091 this_sequence A165322 A082305 A144263
Adjacent sequences: A145299 A145300 A145301 this_sequence A145303 A145304 A145305
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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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