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Search: id:A165224
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| A165224 |
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a(0)=1, a(1)=9, a(n)=18*a(n-1)-49*a(n-2) for n>1 . |
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2
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| 1, 9, 113, 1593, 23137, 338409, 4957649, 72655641, 1064876737, 15607654857, 228758827313, 3352883803641, 49142725927201, 720277760311209, 10557006115168913, 154732499817791193, 2267891697076964737
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)/a(n-1) tends to 9+4*sqrt(2) = 14.65685424... [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 25 2009]
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FORMULA
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G.f.: (1-9x)/(1-18x+49x^2) ; E.g.f.: exp(9x)cosh(4sqrt(2)x) ; a(n)= sum{k=0..n, 8^k*binomial(2n,2k)} = sum{k=0..n, 8^k*A086645(n,k)} ; a(n)= 7^n*T(n,9/7) where T is the Chebyshev polynomial of first kind ; a(n) = (1+sqrt(8))^(2n)/2+(1-sqrt(8))^(2n)/2 .
a(n) = ((9-4*sqrt(2))^n+(9+4*sqrt(2))^n)/2. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 25 2009]
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CROSSREFS
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Cf. A081294, A001541, A090965, A083884, A099140, A099141, A099142, A026244
Sequence in context: A143167 A156949 A155624 this_sequence A012116 A157551 A157570
Adjacent sequences: A165221 A165222 A165223 this_sequence A165225 A165226 A165227
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 08 2009
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EXTENSIONS
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More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 25 2009
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