Search: id:A124174
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%I A124174
%S A124174 0,1,10,45,351,1540,11935,52326,405450,1777555,13773376,60384555,
%T A124174 467889345,2051297326,15894464365,69683724540,539943899076,
%U A124174 2367195337045,18342198104230,80414957735001,623094791644755
%N A124174 Sophie Germain triangular numbers tr: 2*tr+1 is also a triangular number.
%C A124174 a(n)=(A124124[[n]]^2+A124124[[n]]-2)/4.
%F A124174 a(n)=35(a(n-2)-a(n-4))+a(n-6).
%F A124174 Formulae from Peter Pein, Dec 04 2006:
%F A124174 a(n)=-11/32 + (-3 - 2*sqrt(2))^n/64 + (5*(3 - 2*sqrt(2))^n)/32 + (-3 
               - 2*sqrt(2))^n/(32*sqrt(2)) - (5*(3 - 2*sqrt(2))^n)/(32*sqrt(2)) 
               + (-3 + 2*sqrt(2))^n/64 - (-3 + 2*sqrt(2))^n/(32*sqrt(2)) + (5*(3 
               + 2*sqrt(2))^n)/32 + (5*(3 + 2*sqrt(2))^n)/(32*sqrt(2))
%F A124174 O.g.f.: (x*(1 + 9*x + x^2))/((1 - x)*(1 - 6*x + x^2)*(1 + 6*x + x^2))
%F A124174 E.g.f.: (-22*exp(x) + exp(-3*x + 2*x*sqrt(2))*(1 - sqrt(2)) - 5*exp(3*x 
               - 2*x*sqrt(2))*(-2 + sqrt(2)) + exp(-3*x - 2*x*sqrt(2))*(1 + sqrt(2)) 
               + 5*exp(3*x + 2*x*sqrt(2))*(2 + sqrt(2)))/64
%F A124174 a(n)=34a(n-2)-a(n-4)+11 [From Kieren MacMillan (kieren(AT)alumni.rice.edu), 
               Nov 08 2008]
%p A124174 a:= n-> (Matrix([[10, 1, 0, 0, 1]]). Matrix(5, (i, j)-> if i=j-1 then 
               1 elif j=1 then [1, 34, -34, -1, 1][i] else 0 fi)^n)[1, 4]: seq (a(n), 
               n=1..30); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 27 
               2009]
%Y A124174 Cf. A005384, A077442, A124124.
%Y A124174 Sequence in context: A141499 A061772 A032165 this_sequence A044112 A073248 
               A044493
%Y A124174 Adjacent sequences: A124171 A124172 A124173 this_sequence A124175 A124176 
               A124177
%K A124174 nice,nonn
%O A124174 1,3
%A A124174 Zak Seidov (zakseidov(AT)gmail.com), Dec 04 2006
%E A124174 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 27 2009

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