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A048900
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Heptagonal pentagonal numbers.
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2
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1, 4347, 16701685, 64167869935, 246532939589097, 947179489733441251, 3639063353022941697757, 13981280455134652269341655, 53716075869563980995868941265, 206377149509584359851476202998987
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OFFSET
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1,2
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COMMENTS
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As n increases, this sequence is approximately geometric with common ratio r=lim(n->Infinity,a(n)/a(n-1))=(4+sqrt(15))^4=1921+496*sqrt(15). - Ant King, Dec 15 2011
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LINKS
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Table of n, a(n) for n=1..10.
Eric Weisstein's World of Mathematics, Heptagonal Pentagonal Number.
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FORMULA
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From Ant King, Dec 15 2011: (Start)
a(n) = 3843*a(n-1) - 3843*a(n-2) + a(n-3).
a(n) = 3842*a(n-1) - a(n-2) + 512.
a(n) = 1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3)+ (2-sqrt(15))^2*(4-sqrt(15))^(4n-3)-32).
a(n) = floor(1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3))).
GF: x*(1+504*x+7*x^2)/((1-x)*(1-3842*x+x^2)).
(End)
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MATHEMATICA
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LinearRecurrence[{3843, -3843, 1}, {1, 4347, 16701685}, 10] (* Ant King, Dec 15 2011 *)
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CROSSREFS
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Cf. A046198, A046199.
Sequence in context: A172884 A172915 A145916 * A170786 A223378 A068292
Adjacent sequences: A048897 A048898 A048899 * A048901 A048902 A048903
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KEYWORD
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nonn,easy
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AUTHOR
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Eric W. Weisstein
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STATUS
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approved
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