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Search: id:A082840
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| -1, 1, 8, 34, 131, 493, 1844, 6886, 25703, 95929, 358016, 1336138, 4986539, 18610021, 69453548, 259204174, 967363151, 3610248433, 13473630584, 50284273906, 187663465043, 700369586269, 2613814880036, 9754889933878, 36405744855479, 135868089488041
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Apart from the initial -1, these are the numbers k such that the triangular number k(k+1)/2 is the sum of three consecutive triangular numbers - see A129803. - Brian Nowell <brianjnow@iinet.net.au>, Nov 03 2009
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FORMULA
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a(n) = A001571(n) - 1. - njas, Nov 03 2009
G.f.: (-1+6x-2x^2)/((1-x)(1-4x+x^2)). With a=2+sqrt(3), b=2-sqrt(3): a(n)=-3/2+(1/12)(a-2b+5)a^n+(1/12)(b-2a+5)b^n. a(n)=-3/2 +(3/4)A003500(n)- (1/4)A003500(n-1). a(n)=(1/2)(A001834(n)-3).
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CROSSREFS
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Sequence in context: A033455 A053298 A124843 this_sequence A101644 A126395 A158991
Adjacent sequences: A082837 A082838 A082839 this_sequence A082841 A082842 A082843
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KEYWORD
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easy,sign,new
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Apr 14 2003
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