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A131557
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Triangular numbers that are the sums of five consecutive triangular numbers.
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9
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55, 2485, 17020, 799480, 5479705, 257429395, 1764447310, 82891465030, 568146553435, 26690794309585, 182941425758080, 8594352876220660, 58906570947547645, 2767354935348742255, 18967732903684582930, 891079694829418784770, 6107551088415488155135
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OFFSET
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1,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..250
Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).
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FORMULA
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The subsequences with odd indices and even indices satisfy the same recurrence relations: a(n+2) = 322*a(n+1)-a(n)-680 and a(n+1) = 161*a(n) -340+9*(320*a(n)^2-1360*a(n)-175)^0.5.
G.f.: -5*x*(11+486*x-635*x^2+2*x^4) / ( (x-1)*(x^2+18*x+1)*(x^2-18*x+1) ).
8*a(n) = 17 +45*A007805(n) +18*(-1)^n*A049629(n). - R. J. Mathar, Apr 28 2020
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EXAMPLE
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a(1) = 55 = 3+6+10+15+21.
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MAPLE
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a:= n-> `if`(n<2, [0, 55][n+1], (<<0|1|0>, <0|0|1>, <1|-323|323>>^iquo(n-2, 2, 'r'). `if`(r=0, <<2485, 799480, 257429395>>, <<17020, 5479705, 1764447310>>))[1, 1]): seq (a(n), n=1..20); # Alois P. Heinz, Sep 25 2008, revised Dec 15 2011
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MATHEMATICA
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LinearRecurrence[{1, 322, -322, -1, 1}, {55, 2485, 17020, 799480, 5479705}, 20] (* Jean-François Alcover, Oct 05 2019 *)
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CROSSREFS
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Cf. A129803.
Sequence in context: A215860 A020536 A212788 * A231853 A119166 A027548
Adjacent sequences: A131554 A131555 A131556 * A131558 A131559 A131560
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KEYWORD
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nonn,easy
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AUTHOR
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Richard Choulet, Oct 06 2007
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EXTENSIONS
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More terms from Alois P. Heinz, Sep 25 2008
Corrected a(6) and a(8), Harvey P. Dale, Oct 02 2011
a(10), a(12), a(14) corrected at suggestion of Harvey P. Dale by D. S. McNeil, Oct 02 2011
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STATUS
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approved
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