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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
OFFSET
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*sqrt(320*a(n)^2 - 1360*a(n) - 175).
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
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Oct 06 2007
EXTENSIONS
More terms from Alois P. Heinz, Sep 25 2008
a(6) and a(8) corrected by Harvey P. Dale, Oct 02 2011
a(10), a(12), a(14) corrected at the suggestion of Harvey P. Dale by D. S. McNeil, Oct 02 2011
STATUS
approved