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Search: id:A154148
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| A154148 |
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Indices k such that 21 plus the k-th triangular number is a perfect square. |
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+0
2
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| 5, 7, 40, 50, 237, 295, 1384, 1722, 8069, 10039, 47032, 58514, 274125, 341047, 1597720, 1987770
(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)=(5,7,40,50); a(n>4)=6*a(n-2)-a(n-4)+2. [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 13 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: 21+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*(-5-2*x-3*x^2+2*x^3+6*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)) = (12+(12+25*x)/(x^2-2*x-1)+1/(x-1)+(-1-10*x)/(x^2+2*x-1))/2 .
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EXAMPLE
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5*(5+1)/2+21 = 6^2. 7*(7+1)/2+21 = 7^2. 40*(40+1)/2+21 = 29^2. 50*(50+1)/2+21 = 36^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A081851 A006067 A147760 this_sequence A153376 A167205 A123781
Adjacent sequences: A154145 A154146 A154147 this_sequence A154149 A154150 A154151
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KEYWORD
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nonn,less,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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