login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A128922 Numbers simultaneously 10-gonal and centered 10-gonal. 3
1, 451, 145351, 46802701, 15070324501, 4852597686751, 1562521384809451, 503127033310956601, 162005342204743216201, 52165217062894004660251, 16797037888909664757384751 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..10.

S. C. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, Mathematics Magazine,  Vol. 84, No. 5, December 2011, pp. 339-350.

Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

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.: z*(1+128*z+z^2)/((1-z)*(1-322*z+z^2)). - Richard Choulet, 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. [Paolo P. Lava, 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, A048909.

Sequence in context: A269763 A020268 A066322 * A224560 A224568 A224561

Adjacent sequences:  A128919 A128920 A128921 * A128923 A128924 A128925

KEYWORD

easy,nonn

AUTHOR

Steven Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 08:57 EDT 2019. Contains 327128 sequences. (Running on oeis4.)