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A133694
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(1/2) * (3*n^2 + 3*n - 4).
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2
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1, 7, 16, 28, 43, 61, 82, 106, 133, 163, 196, 232, 271, 313, 358, 406, 457, 511, 568, 628, 691, 757, 826, 898, 973, 1051, 1132, 1216, 1303, 1393, 1486, 1582, 1681, 1783, 1888, 1996, 2107, 2221, 2338, 2458, 2581, 2707, 2836, 2968, 3103, 3241, 3382, 3526, 3673
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Binomial transform of 1, 6, 3 followed by A000004, i.e. 1, 6, 3, 0, 0, 0, 0,....
Row sums of triangle A133981 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 30 2007
Equals (1, 2, 3, 4,...) convolved with (1, 5, 3, 3, 3,...). Example: a(4) = (1, 2, 3, 4) dot (3, 3, 5, 1) = (3 + 6 + 15 + 4) = 28. - Gary W. Adamson (qntmpkt(AT)yahoo.com), May 01 2009
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FORMULA
| a(n) = a(n-1)+3*n (with a(1)=1). [From Vincenzo Librandi, Nov 23 2010]
a(n) = 3*A000217(n) - 2.
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EXAMPLE
| a(3) = 3*A000217(3)-2 = 3*6-2 = 16.
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MATHEMATICA
| s=1; lst={}; Do[s+=n-3; If[s>0, AppendTo[lst, s]], {n, 0, 6!, 3}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 04 2008]
Table[(3*n^2 + 3*n - 4)/2, {n, 100}]
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PROG
| (MAGMA) a000217:=func< n | n*(n+1) div 2 >; [ 3*a000217(n)-2: n in [1..60] ];
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CROSSREFS
| Cf. A000217 (triangular numbers), A000004 (zero sequence), A133981.
Sequence in context: A119461 A028560 A190530 * A024627 A180724 A140511
Adjacent sequences: A133691 A133692 A133693 * A133695 A133696 A133697
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 20 2007
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EXTENSIONS
| More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 04 2008
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 23 2010
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