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A076140 Triangular numbers T(k) that are three times another triangular number: T(k) such that T(k)=3*T(m) for some m. 9
0, 3, 45, 630, 8778, 122265, 1702935, 23718828, 330360660, 4601330415, 64088265153, 892634381730, 12432793079070, 173166468725253, 2411897769074475, 33593402298317400, 467895734407369128, 6516946879404850395, 90769360577260536405, 1264254101202242659278 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is a subsequence of A045943. - Michel Marcus, Apr 26 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

FORMULA

Closed form: a(n)=(3/288)*(-24+(12-6*sqrt(3))*(7-4*sqrt(3))^n+(12+6*sqrt(3))*(7+4*sqrt(3))^n).

Recurrence: a(0)=0, a(1)=3, a(2)=45; a(n) = 15*(a(n-1)-a(n-2))+a(n-3) for n>=3. G.f.: 3/(1-15*x+15*x^2-x^3). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002

a(n) = 3*A076139(n) = 3/2*A217855(n) = 3/4*A123480(n) = 3/8*A045899(n). - Peter Bala, Dec 31 2012

EXAMPLE

a(3)=630 because 630=T(35) and 630/3=210=T(20).

MATHEMATICA

Join[{0}, CoefficientList[Series[3/(1-15x+15x^2-x^3), {x, 0, 20}], x]]  (* Harvey P. Dale, Apr 02 2011 *)

PROG

(PARI) concat(0, Vec(-3*x/((x-1)*(x^2-14*x+1)) + O(x^100))) \\ Colin Barker, May 15 2015

CROSSREFS

The m values are in A061278 and the k values are in A001571.

Cf. A076139, A045899, A123480, A217855.

Sequence in context: A271236 A270064 A141445 * A131568 A287031 A124487

Adjacent sequences:  A076137 A076138 A076139 * A076141 A076142 A076143

KEYWORD

easy,nonn

AUTHOR

Bruce Corrigan (scentman(AT)myfamily.com), Oct 31 2002

EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002

STATUS

approved

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)