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A370175
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a(n) = floor(x*a(n-1)) for n > 0 where x = (5+3*sqrt(5))/2, a(0) = 1.
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0
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1, 5, 29, 169, 989, 5789, 33889, 198389, 1161389, 6798889, 39801389, 233001389, 1364013889, 7985076389, 46745451389, 273652638889, 1601990451389, 9378215451389, 54901029513889, 321396224826389, 1881486271701389, 11014412482638889, 64479493771701389
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OFFSET
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0,2
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COMMENTS
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x = A090550 = 1 + 3*phi = 5.854101966..., where phi is the golden ratio.
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - 5*a(n-3), a(0) = 1, a(1) = 5, a(2) = 29.
a(n) = 5*a(n-1) + 5*a(n-2) - 1.
a(n) = (4*(5-2*sqrt(5))*((5-3*sqrt(5))/2)^n + 4*(5+2*sqrt(5))*((5+3*sqrt(5))/2)^n + 5)/45.
G.f.: (1 - x - x^2)/(1 - 6*x + 5*x^3).
a(n) = Sum_{k = 0..n} A370174(n,k)*4^k.
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EXAMPLE
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a(0) = 1, a(1) = floor(x) = 5 where x = (5+3*sqrt(5))/2.
a(2) = floor(5*x) = 29, a(3) = floor(29*x) = 169.
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CROSSREFS
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KEYWORD
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nonn,easy,new
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AUTHOR
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STATUS
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approved
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