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 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)