A221703 Let K be a local ring with a principal maximal ideal J of nilpotent degree 3 with |K/J|>2; a(n) = number of D-invariant ideals in the ring R_n(K,J).

14, 66, 300, 1326, 5750, 24604, 104268, 438678, 1835260, 7643708, 31719544, 131230924, 541549798, 2229948752, 9165030668, 37606175462, 154083290228, 630512206892, 2577105061928, 10522561454372, 42924408013628, 174951432818024, 712513363073720, 2899738101749116, 11793408213411000, 47935401657804504, 194728337295807856

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..110

Formula

Conjecture: (n+2) *(101496*n^2 -9493711*n +47969511) *a(n) +8 *(12687*n^3 +14002447*n^2 -60550969*n -45758370) *a(n-1) +4*( -1420944*n^3 -111890800*n^2 +622530778*n -414036471) *a(n-2) +48*(2*n-7) *(152244*n^2 +6705204*n -18873683) *a(n-3)=0. - R. J. Mathar, Mar 15 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, 3), n=2..40)];

Prog

(Maxima) A221703(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(A221703(n, 3), n, 2, 40); /* Martin Ettl, Jan 24 2013 */

Crossrefs

Sequence in context: A336744 A249291 A280401 * A064096 A250141 A071616

Adjacent sequences: A221700 A221701 A221702 * A221704 A221705 A221706

Keyword

nonn

Author

N. J. A. Sloane, Jan 22 2013

Status

approved