%I A133142
%S A133142 1,1201,1731661,2497053781,3600749820361,5192278743906601,
%T A133142 7487262347963498101,10796627113484620354861,15568728810382474588211281,
%U A133142 22450096147944414871580312161,32373023076607035862344221924701
%N A133142 Numbers which are both centered square and decagonal numbers.
%C A133142 We solve r^2+(r+1)^2=5*p^2-5*p+1 equivalent to 2*(2*r+1)^2=5*(2*p-1)^2-3. 
               the Diophantine equation (2*X)^2=10*Y^2-6 is such that
%C A133142 X is given by 1, 49,1861,70669,... with a(n+2)=38*a(n+1)-a(n) and also 
               a(n+1)=19*a(n)+(360*a(n)^2+540)^0.5
%C A133142 Y is given by 1, 31,1177,44695,... with a(n+2)=38*a(n+1)-a(n) and also 
               a(n+1)=19*a(n)+(360*a(n)^2-216)^0.5
%C A133142 r is given by 0, 24,930,35334,... with a(n+2)=38*a(n+1)-a(n)+18 and also 
               a(n+1)=19*a(n)+9+(360*a(n)^2+360*a(n)+225)^0.5 (new sequence it seems)
%C A133142 p is given by 1, 16,589, 22345,... with a(n+2)=38*a(n+1)-a(n)-18 and 
               also a(n+1)=19*a(n)-9+(360*a(n)^2-360*a(n)+36)^0.5 (new sequence 
               it seems)
%F A133142 a(n+2)=1442*a(n+1)-a(n)-180, a(n+1)=721*a(n)-90+38*(360*a(n)^2-90*a(n)-45)^0.5. 
               G.f.: f(z)=a(1)*z+a(2)*z^2+...=((z*(1-242*z+z^2))/((1-z)*(1-442*z+z^2))
%F A133142 a(n)=(1/8)+(7/16)*[721-228*sqrt(10)]^n-(1/8)*[721-228*sqrt(10)]^n*sqrt(10)+(1/
               8)*[721+228 *sqrt(10)]^n*sqrt(10)+(7/16)*[721+228*sqrt(10)]^n, with 
               n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 26 2008]
%Y A133142 Sequence in context: A107520 A020390 A156620 this_sequence A068534 A135239 
               A046043
%Y A133142 Adjacent sequences: A133139 A133140 A133141 this_sequence A133143 A133144 
               A133145
%K A133142 nonn
%O A133142 1,2
%A A133142 Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 21 2007, corrected 
               Sep 29 2007
%E A133142 More terms from Paolo P. Lava (ppl(AT)spl.at), Sep 26 2008