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A103220
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n*(n+1)*(3*n^2+n-1)/6 .
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6
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0, 1, 13, 58, 170, 395, 791, 1428, 2388, 3765, 5665, 8206, 11518, 15743, 21035, 27560, 35496, 45033, 56373, 69730, 85330, 103411, 124223, 148028, 175100, 205725, 240201, 278838, 321958, 369895, 422995, 481616, 546128, 616913, 694365, 778890
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums of A103219.
Contribution from Bruno Berselli, Dec 10 2010: (Start)
a(n) = n*A002412(n)-sum[A002412(i), i=0..n-1]. More generally: n^2*(n+1)*(2*d*n-2*d+3)/6 -sum[i*(i+1)*(2*d*i-2*d+3), i=0..n-1]/6 = n *(n+1) *(3*d*n^2-d*n+4*n-2*d+2)/12; in this sequence is d=2.
The inverse binomial transform yields 0, 1, 11, 22, 12, 0, 0 (0 continued). (End)
a(n-1) is also number of ways to place 2 nonattacking semi-queens (see A099152) on an n X n board - from Vaclav Kotesovec (kotesovec(AT)chello.cz), Dec 22 2011.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| G.f.: -x*(1+8*x+3*x^2)/(x-1)^5.
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MAPLE
| for(n=0, 100, print1((3*n^4+4*n^3-n)/6, ", "))
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CROSSREFS
| Cf. A103219, A002412, A002418.
Sequence in context: A147019 A183317 A055833 * A086221 A171749 A141917
Adjacent sequences: A103217 A103218 A103219 * A103221 A103222 A103223
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KEYWORD
| easy,nonn
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AUTHOR
| Lambert Klasen (lambert.klasen(AT)gmx.de) and Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 25 2005
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