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A128119
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Square array T(n,m) read by antidiagonals: number of sublattices of index n in generic m-dimensional lattice.
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0
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1, 1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 13, 7, 1, 1, 31, 40, 35, 6, 1, 1, 63, 121, 155, 31, 12, 1, 1, 127, 364, 651, 156, 91, 8, 1, 1, 255, 1093, 2667, 781, 600, 57, 15, 1, 1, 511, 3280, 10795, 3906, 3751, 400, 155, 13, 1, 1, 1023, 9841, 43435, 19531, 22932, 2801, 1395
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,5
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COMMENTS
| Differs from sum of divisors of m^(n-1) in 4th column!
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LINKS
| Yi Ming Zhou, Gaussian binomials and the number of sublattices
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FORMULA
| Dirichlet g.f.: prod(i=0,m-1, zeta(s-i) ).
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EXAMPLE
| Array starts:
1,1,1,1,1,1,1,1,1,
1,3,4,7,6,12,8,15,13,
1,7,13,35,31,91,57,155,130,
1,15,40,155,156,600,400,1395,1210,
1,31,121,651,781,3751,2801,11811,11011,
1,63,364,2667,3906,22932,19608,97155,99463,
1,127,1093,10795,19531,138811,137257,788035,896260,
1,255,3280,43435,97656,836400,960800,6347715,8069620,
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PROG
| (PARI) T(n, m)=local(k, v); v=factor(m); k=matsize(v)[1]; prod(i=1, k, prod(j=1, n-1, (v[i, 1]^(v[i, 2]+j)-1)/(v[i, 1]^j-1)))
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CROSSREFS
| Rows include A000203, A001001, A038991, A038992, A038993, A038994, A038995, A038996, A038997, A038998, A038999.
Columns include A000225, A003462, A006095, A003463, A023000, A006096, A006100, A046915.
Sequence in context: A140068 A179745 A121300 * A158198 A158793 A112996
Adjacent sequences: A128116 A128117 A128118 * A128120 A128121 A128122
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, May 09 2007
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EXTENSIONS
| Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 28 2009
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