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Search: id:A128922
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| A128922 |
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Numbers simultaneously 10-gonal and centered 10-gonal. |
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+0
2
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| 1, 451, 145351, 46802701, 15070324501, 4852597686751, 1562521384809451, 503127033310956601, 162005342204743216201, 52165217062894004660251, 16797037888909664757384751
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, submitted.
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FORMULA
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Let x(n) + y(n)*sqrt(80) =: (10+sqrt(80))*(9+sqrt(80))^n, s(n) = (y(n)+1)/2; then a(n) = (1/2)*(2+10*(s(n)^2-s(n)))
a(n+2)=322*a(n+1)-a(n)+130, a(n+1)=161*a(n)+65+9*(320*a(n)^2+260*a(n)+45)^0.5. G.f.: f(z)=a(1)*z+a(2)*z^2+...=((z*(1+128*z+z^2))/((1-z)*(1-322*z+z^2)) - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 01 2007
a(n)=-(13/32)+(45/64)*[161-72*sqrt(5)]^n-(5/16)*[161-72*sqrt(5)]^n*sqrt(5)+(45/64)*[161+72 *sqrt(5)]^n+(5/16)*sqrt(5)*[161+72*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 26 2008]
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EXAMPLE
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a(1) = 451 because 451 is the tenth centered 10-gonal number and the eleventh 10-gonal number.
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MAPLE
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CP := n -> 1+1/2*10*(n^2-n): N:=10: u:=9: v:=1: x:=10: y:=1: k_pcp:=[1]: for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+80*tempy*v: y:=tempx*v+tempy*u: s:=(y+1)/2: k_pcp:=[op(k_pcp), CP(s)]: end do: k_pcp;
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CROSSREFS
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Cf. A001107, A062786.
Sequence in context: A145492 A020268 A066322 this_sequence A116308 A081739 A076547
Adjacent sequences: A128919 A128920 A128921 this_sequence A128923 A128924 A128925
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KEYWORD
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easy,nonn
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AUTHOR
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Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
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