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A071239
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a(n) = n*(n+1)*(n^2+2)/6.
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6
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0, 1, 6, 22, 60, 135, 266, 476, 792, 1245, 1870, 2706, 3796, 5187, 6930, 9080, 11696, 14841, 18582, 22990, 28140, 34111, 40986, 48852, 57800, 67925, 79326, 92106, 106372, 122235, 139810, 159216, 180576, 204017, 229670, 257670, 288156, 321271, 357162, 395980
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OFFSET
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0,3
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COMMENTS
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Number of binary pattern classes with 4 black beads in the (2,n)-rectangular grid; two patterns are in the same class if one of them can be obtained by reflection or rotation of the other one. - Yosu Yurramendi, Sep 12 2008
This sequence is the case k=n+3 of b(n,k) = n*(n+1)*((k-2)*n-(k-5))/6, which is the n-th k-gonal pyramidal number. Therefore, apart from 0, this sequence is the 3rd diagonal of the array in A080851. - Luciano Ancora, Apr 10 2015
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REFERENCES
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T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
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LINKS
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FORMULA
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a(n) = 5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5), n>4. - Harvey P. Dale, May 01 2013
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MATHEMATICA
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Table[(n(n+1)(n^2+2))/6, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 6, 22, 60}, 40] (* Harvey P. Dale, May 01 2013 *)
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PROG
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(R) a <- vector()
for(n in 1:40) a[n] <- (1/4)*(choose(2*n, 4) + 3*choose(n, 2))
a
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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