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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 (list; graph; refs; listen; history; text; internal format)
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 *)

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 A121898

Adjacent sequences:  A257709 A257710 A257711 * A257713 A257714 A257715

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 05 2015

STATUS

approved

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)