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Search: id:A154140
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| A154140 |
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Indices k such that 6 plus the k-th triangular number is a perfect square. |
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+0
4
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| 2, 4, 19, 29, 114, 172, 667, 1005, 3890, 5860, 22675, 34157, 132162, 199084, 770299, 1160349
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(1..4)=(2,4,19,29); a(n>4)=6*a(n-2)-a(n-4)+2. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 10 2009]
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LINKS
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F. T. Adams-Watters, SeqFan Discussion, Oct 2009
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FORMULA
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{k: 6+k*(k+1)/2 in A000290}
Conjecture: a(n)= +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
Conjecture: G.f.: x*(-2-2*x-3*x^2+2*x^3+3*x^4)/((x-1)* (x^2-2*x-1)* (x^2+2*x-1)) = =(6+(-1-4*x)/(x^2+2*x-1)+(6+13*x)/(x^2-2*x-1)+1/(x-1))/2.
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EXAMPLE
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2*(2+1)/2+6 = 3^2. 4*(4+1)/2+6 = 4^2. 19*(19+1)/2+6 = 14^2. 29*(29+1)/2+6 = 21^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A009418 A153691 A056727 this_sequence A131578 A018273 A047092
Adjacent sequences: A154137 A154138 A154139 this_sequence A154141 A154142 A154143
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KEYWORD
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nonn,more,new
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 18 2009
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