login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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