This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A128922 #24 Jan 06 2024 01:00:20 %S A128922 1,451,145351,46802701,15070324501,4852597686751,1562521384809451, %T A128922 503127033310956601,162005342204743216201,52165217062894004660251, %U A128922 16797037888909664757384751 %N A128922 Numbers simultaneously 10-gonal and centered 10-gonal. %H A128922 S. C. Schlicker, <a href="http://www.jstor.org/stable/10.4169/math.mag.84.5.339">Numbers Simultaneously Polygonal and Centered Polygonal</a>, Mathematics Magazine, Vol. 84, No. 5, December 2011, pp. 339-350. %H A128922 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (323,-323,1). %F A128922 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))). %F A128922 From _Richard Choulet_, Oct 01 2007: (Start) %F A128922 a(n+2) = 322*a(n+1)-a(n)+130. %F A128922 a(n+1) = 161*a(n)+65+9*(320*a(n)^2+260*a(n)+45)^0.5. %F A128922 G.f.: z*(1+128*z+z^2)/((1-z)*(1-322*z+z^2)). (End) %e A128922 a(1) = 451 because 451 is the tenth centered 10-gonal number and the eleventh 10-gonal number. %p A128922 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; %Y A128922 Cf. A001107, A062786, A048909. %K A128922 easy,nonn %O A128922 0,2 %A A128922 _Steven Schlicker_, Apr 24 2007