A221701 Let K be a local ring with a principal maximal ideal J of nilpotent degree 2 with |K/J|>2; a(n) = number of D-invariant ideals in the ring R_n(K,J).

8, 36, 160, 696, 2978, 12592, 52788, 219888, 911480, 3763832, 15494608, 63627024, 260733598, 1066567352, 4356387548, 17770522592, 72407072528, 294732200792, 1198639773728, 4870853772752, 19779319412708, 80266979450624, 325542118876520, 1319605521277216, 5346467285085648, 21651719411554992, 87646668885161696, 354657520759569056

Offset

2,1

References

G. P. Egorychev et al., Enumeration of ideals of some nilpotent matrix rings, J. Algebra and Applications, 12 (2013), #1250140.

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..100

Formula

Conjecture: (n+4) *(127*n^2 -82004*n +181245)*a(n) +(127*n^3 +983454*n^2 +469493*n -5725578) *a(n-1) +2*(-3556*n^3 -1976261*n^2 +1650923*n +5023392) *a(n-2) +8*(2*n-3) *(1143*n^2 +332375*n -209308)*a(n-3)=0. - R. J. Mathar, Mar 17 2016

Maple

f:=(n, s)->(2*s*n-s-3*n+1)*binomial(2*n-2, n-1)-(4/n)*binomial(2*n, n-2)+2^(2*n-1);
[seq(f(n, 2), n=2..40)];

Prog

(Maxima) A221701(n, s):=(2*s*n-s-3*n+1)*binomial(2*n-2, n-1)-(4/n)*binomial(2*n, n-2)+2^(2*n-1)$
makelist(A221701(n, 2), n, 2, 40); /* Martin Ettl, Jan 24 2013 */

Crossrefs

Cf. A221703, A221704.

Sequence in context: A344207 A055918 A074404 * A228702 A200667 A200468

Adjacent sequences: A221698 A221699 A221700 * A221702 A221703 A221704

Keyword

nonn

Author

N. J. A. Sloane, Jan 22 2013

Status

approved