A131557 Triangular numbers that are the sums of five consecutive triangular numbers.

55, 2485, 17020, 799480, 5479705, 257429395, 1764447310, 82891465030, 568146553435, 26690794309585, 182941425758080, 8594352876220660, 58906570947547645, 2767354935348742255, 18967732903684582930, 891079694829418784770, 6107551088415488155135

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*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

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

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