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Search: id:A137280
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| A137280 |
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a(n) = 3*a(n-1) + 7*a(n-2). |
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+0
1
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| 1, 10, 37, 181, 802, 3673, 16633, 75610, 343261, 1559053, 7079986, 32153329, 146019889, 663132970, 3011538133, 13676545189, 62110402498, 282067023817, 1280973888937, 5817390833530, 26418989723149, 119978705004157
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) == 1 mod 9.
a(n)/a(n-1) tends to 4.54138126... = (3 + sqrt(37))/2
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FORMULA
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a(1) = 1, a(2) = 10, a(n), n>2 = 3*a(n-1) + 7*a(n-2). a(n) = upper left term in [1,3; 3,2]^n
O.g.f.: x*(1+7*x)/(1-3*x-7*x^2) . a(n)=A015524(n)+7*A015524(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2008
a(n)=-17/74*(3/2-1/2*sqrt(37))^n*sqrt(37)+1/2*(3/2-1/2*sqrt(37))^n+17/74*sqrt(37)*(3 /2+1/2*sqrt(37))^n+1/2*(3/2+1/2*sqrt(37))^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 03 2008
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EXAMPLE
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a(4) = 181 = 3*a(3) + 7*a(2) = 3*37 + 7*10.
a(4) = 181 = upper left term in [1,3; 3,2]^4.
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CROSSREFS
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Adjacent sequences: A137277 A137278 A137279 this_sequence A137281 A137282 A137283
Sequence in context: A048480 A116970 A110528 this_sequence A071261 A129426 A065009
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 14 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2008
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