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A153448
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3 times 12-gonal (or dodecagonal) numbers: 3n(5n-4).
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11
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0, 3, 36, 99, 192, 315, 468, 651, 864, 1107, 1380, 1683, 2016, 2379, 2772, 3195, 3648, 4131, 4644, 5187, 5760, 6363, 6996, 7659, 8352, 9075, 9828, 10611, 11424, 12267, 13140, 14043, 14976, 15939, 16932, 17955, 19008, 20091, 21204
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This sequence is related to A172117 for d=10 in the general formula n*[3*n*(d*n-d+2)/2] - sum{i=0..n-1} 3*i*(d*i-d+2)/2 = n*(n+1)*(2*d*n-2*d+3)/2. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 26 2010]
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LINKS
| B. Berselli, a description of the recursive method in Comment n*Ar(n)-sum[i=0...n-1]Ar(i) (where Ar(m) is the m-th term of the sequence Ar in OEIS): website Matem@ticamente. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 26 2010]
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 15n^2 - 12n = A051624(n)*3.
a(n)=30*n+a(n-1)-27 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 03 2010]
G.f.: 3*x*(1+9*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011
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MATHEMATICA
| s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 3, 7!, 30}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 02 2009]
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CROSSREFS
| Cf. A051624, A152965.
3 times n-gonal numbers: A045943, A033428, A062741, A094159, A152773, A152751, A152759, A152767, A153783, A153875.
Sequence in context: A113799 A072682 A158207 * A140958 A156189 A158077
Adjacent sequences: A153445 A153446 A153447 * A153449 A153450 A153451
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KEYWORD
| easy,nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Dec 26 2008
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