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Search: id:A154145
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| A154145 |
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Indices k such that 15 plus the k-th triangular number is a perfect square. |
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+0
2
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| 1, 4, 6, 11, 20, 33, 43, 70, 121, 196, 254, 411, 708, 1145, 1483, 2398, 4129, 6676, 8646, 13979, 24068, 38913, 50395, 81478, 140281, 226804, 293726, 474891, 817620, 1321913, 1711963
(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)=(1,4,6,11); 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: 15+k*(k+1)/2 in A000290}
Conjecture: a(n)= +a(n-1) +6*a(n-4) -6*a(n-5) -a(n-8) +a(n-9).
Conjecture: G.f.: x*(-1-3*x-2*x^2-5*x^3-3*x^4+5*x^5+2*x^6+3*x^7+2*x^8)/((x-1) * (x^4+2*x^2-1) * (x^4-2*x^2-1)) = (4+(7+4*x+16*x^2+11*x^3)/(x^4-2*x^2-1)+1/(x-1)+(-4-7*x-3*x^2-2*x^3)/(x^4+2*x^2-1))/2 .
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EXAMPLE
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1*(1+1)/2+15 = 4^2. 4*(4+1)/2+15 = 5^2. 6*(6+1)/2+15 = 6^2. 11*(11+1)/2+15 = 9^2.
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CROSSREFS
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Cf. A000217, A000290, A006451.
Sequence in context: A058579 A022318 A047811 this_sequence A091280 A066155 A105308
Adjacent sequences: A154142 A154143 A154144 this_sequence A154146 A154147 A154148
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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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