Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Jan 02 2024 08:54:15
%S 1,793,382537,184382353,88871911921,42836077163881,20646900321079033,
%T 9951763118682930337,4796729176304851343713,2312013511215819664739641,
%U 1114385715676848773553163561,537131602942729893032960097073
%N Numbers which are both 12-gonal and centered 12-gonal numbers.
%C We write G12(r)=5*r^2-4*r and CG12(p)=6*p^2-6*p+1. A number has both properties iff there exist r and p such that 2*(5*r-2)^2=15*(2*p-1)^2+3. The Diophantine equation (2*X)^2=30*Y^2+6 gives 2 new sequences. We obtain also 2 new sequences with the indices given by r and p respectively.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (483,-483,1).
%F a(n+2)=482*a(n+1)-a(n)+312 ; a(n+1)=241*a(n)+156+44*(30*a(n)^2+39*a(n)+12)^0.5 ;
%F G.f.: (z+310*z^2+z^3)/((1-z)*(1-482*z+z^2)).
%t LinearRecurrence[{483,-483,1},{1,793,382537},20] (* _Harvey P. Dale_, Aug 27 2020 *)
%K nonn,easy
%O 1,2
%A _Richard Choulet_, Oct 16 2007