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0, 1, 14, 50, 120, 235, 406, 644, 960, 1365, 1870, 2486, 3224, 4095, 5110, 6280, 7616, 9129, 10830, 12730, 14840, 17171, 19734, 22540, 25600, 28925, 32526, 36414, 40600, 45095, 49910, 55056, 60544, 66385, 72590, 79170, 86136, 93499, 101270
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This sequence is related to the numbers A180223, in fact: 2*a(n) = n*A180223(n) - sum[i=0..n-1] A180223(i). Also 13-gonal (or tridecagonal) pyramidal numbers (see similar sequences in Cross-references). - Bruno Berselli, Dec 14 2010
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189-196.
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LINKS
| B. Berselli, Table of n, a(n) for n = 0..10000. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 19 2010]
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 19 2010]
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FORMULA
| a(n)=n(n+1)(11n-8)/6.
Contribution from Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 19 2010: (Start)
G. f.: x*(1+10*x)/(1-x)^4.
a(n)-4*a(n-1)+6*a(n-2)-4*a(n-3)+a(n-4) = 0 with n>3. (End)
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MATHEMATICA
| Accumulate[Table[n (11n-9)/2, {n, 0, 40}]] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {0, 1, 14, 50}, 40] (* From Harvey P. Dale, Nov 14 2011 *)
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CROSSREFS
| Cf. A051865.
Cf. A180223. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Aug 19 2010]
For n-gonal pyramidal numbers: A172073, A007587, A007586, A007585, A007584, A002414, A002413, A002412, A002411.
Sequence in context: A005914 A009960 A009928 * A205354 A082668 A158519
Adjacent sequences: A050438 A050439 A050440 * A050442 A050443 A050444
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Barry E. Williams, Dec 23 1999
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