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A076140
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Triangular numbers T(k) that are three times another triangular number: T(k) such that T(k)=3*T(m) for some m.
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3
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0, 3, 45, 630, 8778, 122265, 1702935, 23718828, 330360660, 4601330415, 64088265153, 892634381730, 12432793079070, 173166468725253, 2411897769074475, 33593402298317400, 467895734407369128
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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. Generating function: 3/(1-15*x+15*x^2-x^3). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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EXAMPLE
| a(3)=630 because 630=T(35) and 630/3=210=T(20)
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MATHEMATICA
| Join[{0}, CoefficientList[Series[3/(1-15x+15x^2-x^3), {x, 0, 20}], x]] (* From Harvey P. Dale, Apr 02 2011 *)
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CROSSREFS
| The m values are in A061278 and the k values are in A001571
Cf. A076139.
Sequence in context: A061532 A060242 A141445 * A131568 A124487 A132303
Adjacent sequences: A076137 A076138 A076139 * A076141 A076142 A076143
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KEYWORD
| easy,nonn
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AUTHOR
| Bruce Corrigan (scentman(AT)myfamily.com), Oct 31 2002
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EXTENSIONS
| More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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