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A257712
Triangular numbers (A000217) that are the sum of eight consecutive triangular numbers.
6
120, 276, 1176, 28920, 126756, 306936, 1345620, 33362196, 146264856, 354192420, 1552832856, 38499933816, 168789505620, 408737734296, 1791967758756, 44428890250020, 194782943209176, 471682991173716, 2067929240760120, 51270900848577816, 224779347673872036
OFFSET
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))
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 05 2015
STATUS
approved