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%I #34 Dec 21 2016 16:41:55
%S 1,144841,927821665,222590743768705,1425873367156486249,
%T 342076743178546829707489,2191277630703059899650524953,
%U 525702444955366082679116505052393,3367548455158599463971494297793284977,807897836210987628258457093971387133310617
%N 7-gonal numbers which are sum of 2 consecutive 7-gonal numbers.
%C We write (5*p^2-3*p)/2 = (5*r^2-3*r)/2 + (5*(r+1)^2-3*(r+1))/2 ; X=10*p-3 and Y=10*r+2 satisfy the Diophantine equation X^2=2*Y^2+41.
%C Both bisections of the sequence satisfy the recurrence relation b(n+2) = 1536796802*b(n+1)-b(n)-441829080.
%H Colin Barker, <a href="/A133324/b133324.txt">Table of n, a(n) for n = 1..218</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1536796802,-1536796802,-1,1).
%F a(n) = a(n-1)+1536796802*a(n-2)-1536796802*a(n-3)-a(n-4)+a(n-5). - _Colin Barker_, Dec 07 2014
%F G.f.: -x*(697*x^4+167145360*x^3-609119978*x^2+144840*x+1) / ((x-1)*(x^2-39202*x+1)*(x^2+39202*x+1)). - _Colin Barker_, Dec 05 2014
%e a(2) = 2.5*241^2-1.5*241 = 144841 = 5*r^2+4*r+1 with r=170.
%p F:= gfun[rectoproc]({a(n) = a(n-1)+1536796802*a(n-2)-1536796802*a(n-3)-a(n-4)+a(n-5),
%p a(1)=1,a(2)=144841, a(3)=927821665, a(4)=222590743768705, a(5) = 1425873367156486249}, a(n), remember):
%p seq(F(n),n=1..20); # _Robert Israel_, Dec 07 2014
%t LinearRecurrence[{1,1536796802,-1536796802,-1,1},{1,144841,927821665,222590743768705,1425873367156486249},20] (* _Harvey P. Dale_, Dec 21 2016 *)
%o (PARI) Vec(-x*(697*x^4+167145360*x^3-609119978*x^2+144840*x+1) / ((x-1)*(x^2-39202*x+1)*(x^2+39202*x+1)) + O(x^100)) \\ _Colin Barker_, Dec 05 2014
%Y Cf. A000566, A133327, A133328.
%K nonn,easy
%O 1,2
%A _Richard Choulet_, Oct 18 2007
%E More terms from _Colin Barker_, Dec 05 2014
%E Edited by _Michel Marcus_ and _Colin Barker_, Dec 07 2014
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