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A135713
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n*(n+1)*(4*n+1)/2.
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2
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0, 5, 27, 78, 170, 315, 525, 812, 1188, 1665, 2255, 2970, 3822, 4823, 5985, 7320, 8840, 10557, 12483, 14630, 17010, 19635, 22517, 25668, 29100, 32825, 36855, 41202, 45878, 50895, 56265, 62000, 68112, 74613, 81515, 88830, 96570, 104747, 113373, 122460, 132020
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This sequence is related to A045944 by a(n) = n*A045944(n)-sum(k=0..n-1, A045944(k)) = n^2*(3*n+2) -(n-1)*n*(2*n+1)/2; this is the case i=6 in the general formula n^2*(i*n+i-2)/2 - sum(k=0..n-1, k*(i*k+i-2)/2 ) = n*(n+1)*(2*i*n+i-3)/6 . - Bruno Berselli, Nov 19 2010
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REFERENCES
| M. E. Larsen, The eternal triangle - a history of a counting problem, College Math. J., 20 (1989), 370-392.
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LINKS
| B. Berselli, a description of the recursive method in Comments: website Matem@ticamente.
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| O.g.f.: x*(7*x+5)/(x-1)^4. - R. J. Mathar, Apr 22 2008.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3. - Bruno Berselli, Nov 19 2010
a(-n-1) = -A051895(n). - Bruno Berselli, Aug 23 2011
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PROG
| (MAGMA) [n*(n+1)*(4*n+1)/2: n in [0..40]]; // Bruno Berselli, Aug 23 2011
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CROSSREFS
| Bisection of A002717.
Cf. A045944, A160378; A132124, A006331.
Sequence in context: A137116 A137117 A064675 * A085740 A201436 A202508
Adjacent sequences: A135710 A135711 A135712 * A135714 A135715 A135716
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 05 2008
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