

A071239


a(n) = n*(n+1)*(n^2+2)/6.


6



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

0,3


COMMENTS

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)*((k2)*n(k5))/6, which is the nth kgonal pyramidal number. Therefore, apart from 0, this sequence is the 3rd diagonal of the array in A080851.  Luciano Ancora, Apr 10 2015


REFERENCES

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323332, 2002.


LINKS



FORMULA

a(n) = 5*a(n1)10*a(n2)+ 10*a(n3) 5*a(n4)+a(n5), n>4.  Harvey P. Dale, May 01 2013


MATHEMATICA

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 *)


PROG

(R) a < vector()
for(n in 1:40) a[n] < (1/4)*(choose(2*n, 4) + 3*choose(n, 2))
a


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



