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Search: id:A124174
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| A124174 |
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Sophie Germain triangular numbers tr: 2*tr+1 is also a triangular number. |
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+0
1
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| 0, 1, 10, 45, 351, 1540, 11935, 52326, 405450, 1777555, 13773376, 60384555, 467889345, 2051297326, 15894464365, 69683724540, 539943899076, 2367195337045, 18342198104230, 80414957735001, 623094791644755
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)=(A124124[[n]]^2+A124124[[n]]-2)/4.
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FORMULA
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a(n)=35(a(n-2)-a(n-4))+a(n-6).
Formulae from Peter Pein, Dec 04 2006:
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))
O.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
a(n)=34a(n-2)-a(n-4)+11 [From Kieren MacMillan (kieren(AT)alumni.rice.edu), Nov 08 2008]
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MAPLE
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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]
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CROSSREFS
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Cf. A005384, A077442, A124124.
Sequence in context: A141499 A061772 A032165 this_sequence A044112 A073248 A044493
Adjacent sequences: A124171 A124172 A124173 this_sequence A124175 A124176 A124177
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KEYWORD
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nice,nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)gmail.com), Dec 04 2006
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Apr 27 2009
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