A257712 Triangular numbers (A000217) that are the sum of eight consecutive triangular numbers.

120, 276, 1176, 28920, 126756, 306936, 1345620, 33362196, 146264856, 354192420, 1552832856, 38499933816, 168789505620, 408737734296, 1791967758756, 44428890250020, 194782943209176, 471682991173716, 2067929240760120, 51270900848577816, 224779347673872036

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1154,-1154,0,0,-1,1).

Formula

G.f.: -12*x*(3*x^8+7*x^6+13*x^5-3387*x^4+2312*x^3+75*x^2+13*x+10) / ((x-1)*(x^2-6*x+1)*(x^2+6*x+1)*(x^4+34*x^2+1)).

Example

120 is in the sequence because T(15) = 120 = 1+3+6+10+15+21+28+36 = T(1)+ ... +T(8).

Mathematica

LinearRecurrence[{1, 0, 0, 1154, -1154, 0, 0, -1, 1}, {120, 276, 1176, 28920, 126756, 306936, 1345620, 33362196, 146264856}, 30] (* Vincenzo Librandi, Jun 27 2015 *)
Select[Total/@Partition[Accumulate[Range[5*10^6]], 8, 1], OddQ[ Sqrt[ 1+8#]]&] (* The program generates the first 16 terms of the sequence *) (* Harvey P. Dale, Feb 27 2022 *)

Prog

(PARI) Vec(-12*x*(3*x^8+7*x^6+13*x^5-3387*x^4+2312*x^3+75*x^2+13*x+10) / ((x-1)*(x^2-6*x+1)*(x^2+6*x+1)*(x^4+34*x^2+1)) + O(x^100))

Crossrefs

Cf. A000217, A001110, A129803, A131557, A257711, A257713, A259413, A259414, A259415.

Sequence in context: A158130 A070856 A211467 * A250607 A076579 A345350

Adjacent sequences: A257709 A257710 A257711 * A257713 A257714 A257715

Keyword

nonn,easy

Author

Colin Barker, May 05 2015

Status

approved