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Search: id:A154141
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| A154141 |
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Indices k such that 8 plus the k-th triangular number is a perfect square. |
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+0
4
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| 1, 7, 16, 46, 97, 271, 568, 1582, 3313, 9223, 19312, 53758, 112561, 313327, 656056, 1826206
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(1..4)=(1,7,16,46); a(n>4)=6*a(n-2)-a(n-4)+2. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 10 2009]
Also numbers n such that (ceiling(sqrt(n*(n+1)/2)))^2 - n*(n+1)/2 = 8. [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: 8+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*(-1-6*x-3*x^2+6*x^3+2*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = =(4+1/(x-1)-3/(x^2+2*x-1)+(6+15*x)/(x^2-2*x-1))/2.
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EXAMPLE
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1*(1+1)/2+8 = 3^2. 7*(7+1)/2+8 = 6^2. 16*(16+1)/2+8 = 12^2. 46*(46+1)/2+8 = 33^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A055553 A066009 A037241 this_sequence A152530 A065099 A001345
Adjacent sequences: A154138 A154139 A154140 this_sequence A154142 A154143 A154144
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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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