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Search: id:A076140
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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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+0
4
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| 0, 3, 45, 630, 8778, 122265, 1702935, 23718828, 330360660, 4601330415, 64088265153, 892634381730, 12432793079070, 173166468725253, 2411897769074475, 33593402298317400, 467895734407369128
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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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
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a(3)=630 because 630=T(35) and 630/3=210=T(20)
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CROSSREFS
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The m values are in A061278 and the k values are in A001571
Cf. A076139.
Sequence in context: A117972 A061532 A060242 this_sequence A131568 A124487 A132303
Adjacent sequences: A076137 A076138 A076139 this_sequence A076141 A076142 A076143
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KEYWORD
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easy,nonn
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AUTHOR
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Bruce Corrigan (scentman(AT)myfamily.com), Oct 31 2002
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 01 2002
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