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A046179
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Indices of hexagonal numbers which are also pentagonal.
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2
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1, 143, 27693, 5372251, 1042188953, 202179284583, 39221739020101, 7608815190614963, 1476070925240282673, 286350150681424223551, 55550453161271059086173
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| As n increases, this sequence is approximately geometric with common ratio r=lim(n->Infinity,a(n)/a(n-1))=(2+sqrt(3))^4=97+56*sqrt(3). - Ant King, Dec 14 2011
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LINKS
| Eric Weisstein's World of Mathematics, Hexagonal Pentagonal Number
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FORMULA
| a(n) = 194*a(n-1) - a(n-2) - 48; g.f.: (1-52*x+3*x^2)/((1-x)*(1-194*x+x^2)) - Warut Roonguthai (warut822(AT)yahoo.com) Jan 08 2001
a(n)=(1/4)+(3/8)*[97-56*sqrt(3)]^n+(3/8)*[97+56*sqrt(3)]^n-(5/24)*[97-56*sqrt(3)]^n*sqrt(3)+(5 /24)*sqrt(3)*[97+56*sqrt(3)]^n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Sep 26 2008]
From Ant King, Dec 14 2011: (Start)
a(n) = 195*a(n-1) - 195*a(n-2) + a(n-3).
a(n) = 1/24*sqrt(3)*((sqrt(3)-1)*(2+sqrt(3))^(4n-2)+(sqrt(3)+1)* (2-sqrt(3))^(4n-2)+2*sqrt(3)).
a(n) = ceiling(1/24*sqrt(3)*(sqrt(3)-1)*(2+sqrt(3))^(4n-2)).
(End)
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MATHEMATICA
| LinearRecurrence[{195, -195, 1}, {1, 143, 27693}, 11] (* Ant King, Dec 14 2011 *)
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CROSSREFS
| Cf. A046178, A046180.
Sequence in context: A199039 A199235 A029555 * A204683 A205159 A205308
Adjacent sequences: A046176 A046177 A046178 * A046180 A046181 A046182
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KEYWORD
| nonn,easy
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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