A000001 Sophie Germain triangular numbers

[Peter Pein]

zak seidov schrieb:
> Just submitted:
> 
> %I A000001
> %S A000001
> 0,1,10,45,351,1540,11935,52326,405450,1777555,13773376,60384555,467889345,2051297326,15894464365,69683724540,539943899076,2367195337045,18342198104230
> %N A000001 Sophie Germain triangular numbers tr:
> 2*tr+1 is also a triangular number.
> %C A000001 a(n)=(A124124[[n]]^2+A124124[[n]]-2)/4.
> %F A000001 For given a(1..6),
> a(n)=35(a(n-2)-a(n-4))+a(n-6).
> %Y A000001 Cf. A005384,  A077442, A124124.
> 
> 
>  
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well, if you like to add this info:

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))

r.g.f.: (x*(1 + 9*x + x^2))/((1 - x)*(1 - 6*x + x^2)*(1 + 6*x + x^2))

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

Peter