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 A002757 Number of bipartite partitions of n white objects and 8 black ones. (Formerly M5123 N2219) 4
 22, 67, 181, 401, 831, 1576, 2876, 4987, 8406, 13715, 21893, 34134, 52327, 78785, 116982, 171259, 247826, 354482, 502090, 704265, 979528, 1351109, 1849932, 2514723, 3396262, 4557867, 6081466, 8068930, 10650479, 13987419, 18283999 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Number of ways to factor p^n*q^8 where p and q are distinct primes. a(n) = if n <= 8 then A054225(8,n) else A054225(n,8). - Reinhard Zumkeller, Nov 30 2011 REFERENCES M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956, p. 1. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 M. S. Cheema and H. Gupta, Tables of Partitions of Gaussian Integers. National Institute of Sciences of India, Mathematical Tables, Vol. 1, New Delhi, 1956 (Annotated scanned pages from, plus a review) FORMULA a(n) ~ 3*sqrt(3) * n^3 * exp(Pi*sqrt(2*n/3)) / (1120*Pi^8). - Vaclav Kotesovec, Feb 01 2016 MATHEMATICA p = 2; q = 3; b[n_, k_] := b[n, k] = If[n>k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d>k, 0, b[n/d, d]], {d, DeleteCases[Divisors[n], 1|n]}]]; a[n_] := b[p^n*q^8, p^n*q^8]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 17 2014, after Alois P. Heinz *) nmax = 50; CoefficientList[Series[(22 + 23*x + 25*x^2 + 16*x^3 + 4*x^4 - 14*x^5 - 34*x^6 - 50*x^7 - 65*x^8 - 52*x^9 - 32*x^10 + 5*x^11 + 27*x^12 + 57*x^13 + 67*x^14 + 65*x^15 + 42*x^16 + 15*x^17 - 14*x^18 - 34*x^19 - 40*x^20 - 46*x^21 - 26*x^22 - 8*x^23 + 8*x^24 + 11*x^25 + 18*x^26 + 14*x^27 + 9*x^28 + 3*x^29 - 7*x^30 - 7*x^31 - 6*x^32 + 3*x^33 + 3*x^34 - x^35)/((1-x) * (1-x^2) * (1-x^3) * (1-x^4) * (1-x^5) * (1-x^6) * (1-x^7) * (1-x^8)) * Product[1/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 01 2016 *) CROSSREFS Column 8 of A054225. Cf. A005380. Sequence in context: A041946 A303858 A041948 * A041950 A114636 A334034 Adjacent sequences:  A002754 A002755 A002756 * A002758 A002759 A002760 KEYWORD nonn AUTHOR EXTENSIONS Edited by Christian G. Bower, Jan 08 2004 STATUS approved

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)