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 A131557 Triangular numbers that are the sums of five consecutive triangular numbers. 9
 55, 2485, 17020, 799480, 5479705, 257429395, 1764447310, 82891465030, 568146553435, 26690794309585, 182941425758080, 8594352876220660, 58906570947547645, 2767354935348742255, 18967732903684582930, 891079694829418784770, 6107551088415488155135 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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). FORMULA 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 EXAMPLE a(1) = 55 = 3+6+10+15+21. MAPLE 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 MATHEMATICA LinearRecurrence[{1, 322, -322, -1, 1}, {55, 2485, 17020, 799480, 5479705}, 20] (* Jean-François Alcover, Oct 05 2019 *) CROSSREFS Cf. A129803. Sequence in context: A215860 A020536 A212788 * A231853 A119166 A027548 Adjacent sequences:  A131554 A131555 A131556 * A131558 A131559 A131560 KEYWORD nonn,easy AUTHOR Richard Choulet, Oct 06 2007 EXTENSIONS 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 STATUS approved

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)