cp's OEIS Frontend

A155105 Positive numbers appearing in the third column of A155103.

%I A155105 #33 Oct 25 2024 09:54:29
%S A155105 1,4,28,364,9100,445900,43252300,8347693900,3213862151500,
%T A155105 2471459994503500,3798634011551879500,11673202317498925703500
%N A155105 Positive numbers appearing in the third column of A155103.
%F A155105 From _Tristan Cam_, Oct 02 2024: (Start)
%F A155105 a(1) = 1, a(n) = a(n-1)*(1+3*2^(n-2)) (conjectured).
%F A155105 a(n) = Product_{k=1..n-1} 1+3*2^(k-1) = QPochhammer[-3, 2, n-1]. (conjectured). (End)
%p A155105 A155102 := proc(n,k) if n = k then 1 ; elif n =2*k then -k-1 ; else 0; end if; end proc:
%p A155105 A155103 := proc(amx) a := array(1..amx,1..amx) ; a[1,1] := 1/A155102(1,1) ;
%p A155105         for r from 1 to amx do
%p A155105                 for c from 1 to r-1 do a[c,r] := 0 ; end do:
%p A155105                 a[r,r] := 1/A155102(r,r) ;
%p A155105                 for c from r-1 to 1 by -1 do a[r,c] := -add(a[cp,c]*A155102(r,cp),cp=c..r-1)/A155102(r,r) ;
%p A155105                         if c = 3 and a[r,c] <> 0 then print( a[r,c]) ; end if;
%p A155105                 end do:
%p A155105         end do:
%p A155105         return ;
%p A155105 end proc:
%p A155105 A155103(290) ; # _R. J. Mathar_, Dec 07 2010
%o A155105 (PARI) \\ after _R. J. Mathar_
%o A155105 T(n,k)=if(n==k,1,if(n==2*k,-(k+1))); \\ from A155102
%o A155105 \\ First term = 1 omitted
%o A155105 a155103(upto) = my(m=3*2^upto, a=matid(m)); for(r=1, m, forstep(c=r-1, 1, -1, a[r,c]=-sum(cp=c, r-1, a[cp,c]*T(r,cp)); if(c==3 && a[r,c]!=0, print1(a[r,c],", "))));
%o A155105 a155103(8) \\ _Hugo Pfoertner_, Oct 03 2024
%Y A155105 Cf. A155103.
%K A155105 nonn,more
%O A155105 1,2
%A A155105 _Mats Granvik_, Jan 20 2009
%E A155105 Two more terms from _R. J. Mathar_, Dec 07 2010
%E A155105 a(8)-a(12) from _Hugo Pfoertner_, Oct 02 2024