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A046199
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Indices of pentagonal numbers which are also heptagonal.
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2
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1, 54, 3337, 206830, 12820113, 794640166, 49254870169, 3053007310302, 189237198368545, 11729653291539478, 727049266877079081, 45065324893087363534, 2793323094104539460017, 173140966509588359157510
(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) - 10.
a(n) = 1/60*((3*sqrt(15)-5)*(4+sqrt(15))^(2*n-1)-(3*sqrt(15)+5)*(4-sqrt(15))^(2*n-1)+10).
a(n) = ceiling(1/60*(3*sqrt(15)-5)*(4+sqrt(15))^(2*n-1)).
GF: x*(1-9*x-2*x^2)/((1-x)*(1-62*x+x^2)).
(End)
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MATHEMATICA
| LinearRecurrence[{63, -63, 1}, {1, 54, 3337}, 14] (* Ant King, Dec 15 2011 *)
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CROSSREFS
| Cf. A046198, A048900.
Sequence in context: A189200 A042405 A187304 * A007761 A178633 A085482
Adjacent sequences: A046196 A046197 A046198 * A046200 A046201 A046202
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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