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

Author

Richard Choulet, Oct 06 2007

Keywords

• nonn
• easy

Examples

			a(1) = 55 = 3+6+10+15+21.
		

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).

Crossrefs

Cf. A129803.

Programs

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 *)

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

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