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Search: id:A086901
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| A086901 |
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a(1) = a(2) = 1; for n>2, a(n) = 4*a(n-1) + 3*a(n-2). |
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+0
4
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| 1, 1, 7, 31, 145, 673, 3127, 14527, 67489, 313537, 1456615, 6767071, 31438129, 146053729, 678529303, 3152278399, 14644701505, 68035641217, 316076669383, 1468413601183, 6821884412881, 31692778455073, 147236767058935
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(n) = [(c + 5)b^n - (b + 5)c^n]/14, where b = 2 + sqrt(7), c = 2 - sqrt(7)
G.f.: x(1-3x)/(1-4x-3x^2). a(n) = A015530(n) - 3*A015530(n-1) = 1 + 6*sum(k=0, n, A015530(k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 01 2004
a(n+1)=Sum_{k,0<=k<=n}3^(n-k)*A122542(n,k), n>=0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 27 2006
a(n) = upper left term in the 2 X 2 matrix [1,2; 3,3]^(n-1) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 02 2008
a(n)=(1/14)*[2-sqrt(7)]^n*sqrt(7)-(1/14)*sqrt(7)*[2+sqrt(7)]^n+(1/2)*[2-sqrt(7)]^n+(1/2)*[2 +sqrt(7)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 20 2008]
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EXAMPLE
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a(3) = 4(1) + 3(1) = 7; a(4) = 4(7) + 3(1) = 31.
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CROSSREFS
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Sequence in context: A001896 A044049 A005825 this_sequence A003526 A121517 A057620
Adjacent sequences: A086898 A086899 A086900 this_sequence A086902 A086903 A086904
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KEYWORD
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easy,nonn
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AUTHOR
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Rick Powers (rick.powers(AT)mnsu.edu), Sep 18 2003
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EXTENSIONS
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More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 19 2003
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