OFFSET
0,2
LINKS
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))).
From Richard Choulet, Oct 01 2007: (Start)
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)). (End)
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
KEYWORD
easy,nonn
AUTHOR
Steven Schlicker, Apr 24 2007
STATUS
approved