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A046198
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Indices of heptagonal numbers (A000566) which are also pentagonal.
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2
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1, 42, 2585, 160210, 9930417, 615525626, 38152658377, 2364849293730, 146582503552865, 9085750370983882, 563169940497447801, 34907450560470779762, 2163698764808690897425, 134114415967578364860570
(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))=(4+sqrt(15))^2=31+8*sqrt(15). - Ant King, Dec 15 2011
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| From Ant King, Dec 15 2011: (Start)
a(n) = 63*a(n-1) - 63*a(n-2) + a(n-3).
a(n) = 62*a(n-1) - a(n-2) - 18.
a(n) = 1/60*((9-sqrt(15))*(4+sqrt(15))^(2*n-1)+(9+sqrt(15))*(4-sqrt(15))^(2*n-1)+18).
a(n) = ceiling(1/60*(9-sqrt(15))*(4+sqrt(15))^(2*n-1)).
GF: x*(1-21*x+2*x^2)/((1-x)*(1-62*x+x^2)).
(End)
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MATHEMATICA
| LinearRecurrence[{63, -63, 1}, {1, 42, 2585}, 14] (* Ant King, Dec 15 2011 *)
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CROSSREFS
| Cf. A046199, A048900.
Sequence in context: A041841 A187365 A180371 * A181193 A053875 A048538
Adjacent sequences: A046195 A046196 A046197 * A046199 A046200 A046201
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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