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Search: id:A128537
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| A128537 |
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a(n) = denominator of r(n): r(n) is such that, for every positive integer n, the continued fraction (of rational terms) [r(1);r(2),...,r(n)] equals n(n+1)/2, the n-th triangular number. |
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+0
2
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| 1, 2, 3, 16, 5, 128, 525, 2048, 11025, 32768, 10395, 262144, 2081079, 2097152, 19324305, 67108864, 21332025, 2147483648, 25264228275, 17179869184, 224009490705, 137438953472, 218578957597, 2199023255552, 699533769675
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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For n >=4, r(n) = -(2n-1)*(2n-3)/(n(n-2) r(n-1)).
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EXAMPLE
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The 4th triangular number, 10, equals 1 +(1/2 +1/(-10/3 +16/21)).
The 5th triangular number, 15, equals 1 +(1/2 +1/(-10/3 +1/(21/16 -5/16))).
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MAPLE
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L2cfrac := proc(L, targ) local a, i; a := targ ; for i from 1 to nops(L) do a := 1/(a-op(i, L)) ; od: end: A128537 := proc(nmax) local b, n, bnxt; b := [1] ; for n from nops(b)+1 to nmax do bnxt := L2cfrac(b, n*(n+1)/2) ; b := [op(b), bnxt] ; od: [seq( denom(b[i]), i=1..nops(b))] ; end: A128537(26) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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CROSSREFS
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Cf. A128536.
Sequence in context: A088447 A103390 A167761 this_sequence A066841 A074270 A007120
Adjacent sequences: A128534 A128535 A128536 this_sequence A128538 A128539 A128540
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet Mar 09 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
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