|
| |
|
|
A128922
|
|
Numbers simultaneously 10-gonal and centered 10-gonal.
|
|
1
| |
|
|
1, 451, 145351, 46802701, 15070324501, 4852597686751, 1562521384809451, 503127033310956601, 162005342204743216201, 52165217062894004660251, 16797037888909664757384751
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| S. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, submitted.
|
|
|
FORMULA
| 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 (paoloplava(AT)gmail.com), Sep 26 2008]
|
|
|
EXAMPLE
| a(1) = 451 because 451 is the tenth centered 10-gonal number and the eleventh 10-gonal number.
|
|
|
MAPLE
| 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;
|
|
|
CROSSREFS
| Cf. A001107, A062786.
Sequence in context: A145492 A020268 A066322 * A116308 A183636 A205209
Adjacent sequences: A128919 A128920 A128921 * A128923 A128924 A128925
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
|
| |
|
|
