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Search: id:A129803
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| A129803 |
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Triangular numbers which are the sum of three consecutive triangular numbers. |
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7
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| 10, 136, 1891, 26335, 366796, 5108806, 71156485, 991081981, 13803991246, 192264795460, 2677903145191, 37298379237211, 519499406175760, 7235693307223426, 100780206894952201, 1403687203222107385
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Indices m: 4, 16, 61, 229, 856, 3196, 11929, with recurrence m(i)=5(m(i-1)-m(i-2))+m(i-3).
If first term is omitted, same sequence as A128862. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 13 2008
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FORMULA
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a(n)=tr(m)=tr(k)+tr(k+1)+tr(k+2), where tr(k)=k(k+1)/2=A000217(k).
a(n+2)=14*a(n+1)-a(n)-3, a(n+1)=7*a(n)-1.5+0.5*(192*a(n)^2-96*a(n)-15)^0.5. G.f.: f(z)=a(1)*z+a(2)*z^2+...= (10*z-14*z^2+z^3)/((1-z)*(1-14*z+z^2)) - Richard Choulet (richardchoulet(AT)yahoo.fr), Oct 06 2007
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EXAMPLE
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tr(k)=k(k+1)/2=A000217(k): 10=tr(4)=tr(1)+tr(2)+tr(3)=1+3+6,
136=tr(16)=tr(8)+tr(9)+tr(10)=36+45+55,
1891=tr(61)=tr(34)+tr(35)+tr(36)=595+630+666,
26335=tr(229)=tr(131)+tr(132)+tr(133)=8646+8778+8911,
366796=tr(856)=tr(493)+tr(494)+tr(495)=121771+122265+122760.
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CROSSREFS
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Cf. A000217, A128862.
Sequence in context: A050408 A133197 A128862 this_sequence A065024 A026244 A096619
Adjacent sequences: A129800 A129801 A129802 this_sequence A129804 A129805 A129806
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), May 18 2007
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