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A111144
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n*(n+13)*(n+14)/6.
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1
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0, 35, 80, 136, 204, 285, 380, 490, 616, 759, 920, 1100, 1300, 1521, 1764, 2030, 2320, 2635, 2976, 3344, 3740, 4165, 4620, 5106, 5624, 6175, 6760, 7380, 8036, 8729, 9460, 10230, 11040, 11891, 12784, 13720, 14700, 15725, 16796, 17914, 19080, 20295, 21560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Analogous to A111396 n(n+7)(n+8)/6 and A000292 expressed as n(n+1)(n+2)/6. a(13) = 1521 = 39^2. a(14) = 1764 = 42^2. After a(1) all values have at least three prime factors with multiplicity, for example a(33) = 11891 = 11 * 23 * 47 and a(49) = 31899 = 3 * 7^3 * 31.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| G.f.: x*(35-60*x+26*x^2)/(1-x)^4. [Colin Barker, Jan 11 2012]
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MATHEMATICA
| Table[n (n + 13) (n + 14)/6, {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)
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PROG
| (MAGMA) [n*(n+13)*(n+14)/6: n in [0..50]]; // Vincenzo Librandi, Jan 11 2012
(PARI) a(n)=n*(n+13)*(n+14)/6 \\ Charles R Greathouse IV, Jan 11 2012
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CROSSREFS
| a(n) = A000292(n) + 4n^2 + 30n.
Cf. A111396.
Sequence in context: A043205 A043985 A201068 * A044173 A044554 A156126
Adjacent sequences: A111141 A111142 A111143 * A111145 A111146 A111147
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 12 2005
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