This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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