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Search: id:A105036
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| A105036 |
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a(0) = 0, a(1) = 4, a(2) = 8, a(3) = 116, for n>3 a(n) = 26*a(n-2) - a(n-4) + 12. |
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+0
3
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| 0, 4, 8, 116, 220, 3024, 5724, 78520, 148616, 2038508, 3858304, 52922700, 100167300, 1373951704, 2600491508, 35669821616, 67512611920, 926041410324, 1752727418424, 24041406846820, 45503400267116, 624150536607008
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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It appears this sequence gives all the nonnegative m such that 42*n^2 + 42*n + 1 is a square.
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FORMULA
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a(n)=-1/2-1/6*(-1)^n*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4*(-1)^n)*sqrt(42) *(13 + 2*sqrt(42))^(-1/4)-(-1)^n*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4*( -1)^n)*(13 + 2*sqrt(42))^(-1/4) + 5/28*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2*sqrt(42))^(1/4 *(-1)^n)*sqrt(42)*(13 + 2*sqrt(42))^(-1/4) + 5/4*(13 + 2*sqrt(42))^(1/2*n)*(13 + 2 *sqrt(42))^(1/4*(-1)^n)*(13 + 2*sqrt(42))^(-1/4) + 1/6*(-1)^n*(13-2*sqrt(42))^(-1/4) *(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)*sqrt(42) + 5/4*(13-2 *sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)-(-1)^n *(13-2*sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n)-5/28*(13-2*sqrt(42))^(-1/4)*(13-2*sqrt(42))^(1/2*n)*(13-2*sqrt(42))^(1/4*(-1)^n) *sqrt(42), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 28 2009]
G.f.: 4*x*(1+x+x^2)/((1-x)*(x^4-26*x^2+1)). a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2009]
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CROSSREFS
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Sequence in context: A057974 A071277 A111100 this_sequence A012940 A013049 A060239
Adjacent sequences: A105033 A105034 A105035 this_sequence A105037 A105038 A105039
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KEYWORD
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nonn
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AUTHOR
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Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Apr 03 2005
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