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Search: id:A082291
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| A082291 |
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Expansion of x(2+5x-x^2)/((1-x)(1-6x+x^2)). |
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3
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| 2, 19, 118, 695, 4058, 23659, 137902, 803759, 4684658, 27304195, 159140518, 927538919, 5406093002, 31509019099, 183648021598, 1070379110495, 6238626641378, 36361380737779, 211929657785302, 1235216565974039
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Integers n such that (n+1)^2+(n+2)^2 is a square.
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LINKS
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Index entries for two-way infinite sequences
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FORMULA
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G.f.: x(2+5x-x^2)/((1-x)(1-6x+x^2)). a(n)=6a(n-1)-a(n-2)+6. a(-1-n)=-3-a(n).
A001109(n+1)+A001109(n)=2a(n)+3, a(n+1)=7a(n)-4*A001109(n)+9. - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de)
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PROGRAM
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(PARI) a(n)=if(n<0, -3-a(-1-n), if(n==0, -1, polcoeff(x*(2+5*x-x^2)/((1-x)*(1-6*x+x^2))+x*O(x^n), n)))
(PARI) {a(n)=subst(poltchebi(n+1)-poltchebi(n)-6, x, 3)/4}
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CROSSREFS
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Cf. A001652(n)=a(n)+1.
Sequence in context: A055875 A089659 A101253 this_sequence A055518 A089364 A166298
Adjacent sequences: A082288 A082289 A082290 this_sequence A082292 A082293 A082294
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Apr 07 2003
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