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A048903
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Heptagonal hexagonal numbers.
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2
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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)) = (2+sqrt(5))^8 = 51841+23184*sqrt(5). - Ant King, Dec 24 2011
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LINKS
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Table of n, a(n) for n=1..8.
Eric Weisstein's World of Mathematics, Heptagonal Hexagonal Number
Index to sequences with linear recurrences with constant coefficients, signature (103683,-103683,1).
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FORMULA
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Contribution from Ant King, Dec 24 2011: (Start)
G.f.: x*(1+18088*x+55*x^2)/((1-x)*(1-103682*x+x^2)).
a(n) = 103683*a(n-1)-103683*a(n-2)+a(n-3).
a(n) = 103682*a(n-1)-a(n-2)+18144.
a(n) = 1/80*((sqrt(5)-1)*(2+sqrt(5))^(8n-5)- (sqrt(5)+1)*(2-sqrt(5))^(8n-5)-14).
a(n) = floor(1/80*(sqrt(5)-1)*(2+sqrt(5))^(8n-5)).
(End)
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MATHEMATICA
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LinearRecurrence[{103683, -103683, 1}, {1, 121771, 12625478965}, 8]; (* Ant King, Dec 24 2011 *)
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CROSSREFS
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Cf. A048901, A048902.
Sequence in context: A135495 A067384 A066881 * A185864 A115545 A224584
Adjacent sequences: A048900 A048901 A048902 * A048904 A048905 A048906
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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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