A259414 Triangular numbers (A000217) that are the sum of thirteen consecutive triangular numbers.

2080, 414505, 28815436, 49317346, 3428789455, 698283666730, 48548229019381, 83089887991201, 5776831256176630, 1176469718198438755, 81794153348207147926, 139990009467226925656, 9732816854065394603605, 1982118534159467652450580, 137806953149317550935817071

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..641

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1684802,-1684802,0,0,-1,1).

Formula

G.f.: -13*x*(7*x^8 +153*x^6 +31725*x^5 -9608927*x^4 +1577070*x^3 +2184687*x^2 +31725*x +160) / ((x -1)*(x^2 -36*x -1)*(x^2 +36*x -1)*(x^4 +1298*x^2 +1)).

Example

2080 is in the sequence because T(64) = 2080 = 66 + 78 + 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 = T(11) + ... + T(23).

Mathematica

 LinearRecurrence[{1, 0, 0, 1684802, -1684802, 0, 0, -1, 1}, {2080, 414505, 28815436, 49317346, 3428789455, 698283666730, 48548229019381, 83089887991201, 5776831256176630}, 30] (* Vincenzo Librandi, Jun 27 2015 *)

Prog

(PARI) Vec(-13*x*(7*x^8 +153*x^6 +31725*x^5 -9608927*x^4 +1577070*x^3 +2184687*x^2 +31725*x +160) / ((x -1)*(x^2 -36*x -1)*(x^2 +36*x -1)*(x^4 +1298*x^2 +1)) + O(x^20))

Crossrefs

Cf. A000217, A001110, A129803, A131557, A257711, A257712, A257713, A259413, A259415.

Sequence in context: A194605 A233104 A071235 * A233088 A229909 A323813

Adjacent sequences: A259411 A259412 A259413 * A259415 A259416 A259417

Keyword

nonn,easy

Author

Colin Barker, Jun 26 2015

Status

approved