login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293935 Poincaré series for invariant polynomial functions on the space of binary forms of degree 10. 13
1, 0, 1, 0, 2, 0, 6, 0, 12, 5, 24, 13, 52, 33, 97, 80, 177, 160, 319, 301, 540, 547, 887, 926, 1429, 1512, 2219, 2402, 3367, 3681, 5015, 5502, 7294, 8064, 10419, 11550, 14664, 16253, 20287, 22531, 27682, 30738, 37319, 41378, 49671, 55060, 65390, 72391, 85250 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Many of these Poincaré series has every other term zero, in which case these zeros have been omitted.
LINKS
Andries Brouwer, Poincaré Series (See n=10)
EXAMPLE
The Poincaré series is (1 - t^5 + 2t^6 - t^7 + 4t^8 + 4t^9 + 8t^10 + 6t^11 + 16t^12 + 9t^13 + 17t^14 + 15t^15 + 19t^16 + 12t^17 + 23t^18 + 12t^19 + 19t^20 + 15t^21 + 17t^22 + 9t^23 + 16t^24 + 6t^25 + 8t^26 + 4t^27 + 4t^28 - t^29 + 2t^30 - t^31 + t^36) / (1 - t^2)(1 - t^4)(1 - t^5)(1 - t^6)^2(1 - t^7)(1 - t^8)(1 - t^9)
MAPLE
nmax := 120 :
(1 - t^5 + 2*t^6 - t^7 + 4*t^8 + 4*t^9 + 8*t^10 + 6*t^11 + 16*t^12 + 9*t^13 + 17*t^14 + 15*t^15 + 19*t^16 + 12*t^17 + 23*t^18 + 12*t^19 + 19*t^20 + 15*t^21 + 17*t^22 + 9*t^23 + 16*t^24 + 6*t^25 + 8*t^26 + 4*t^27 + 4*t^28 - t^29 + 2*t^30 - t^31 + t^36) / (1 - t^2)/(1 - t^4)/(1 - t^5)/(1 - t^6)^2/(1 - t^7)/(1 - t^8)/(1 - t^9) ;
taylor(%, t=0, nmax) ;
gfun[seriestolist](%) ;
seq( %[1+i], i=0..nmax/2-1) ; # R. J. Mathar, Oct 26 2017
CROSSREFS
For these Poincaré series for d = 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 24 see A097852, A293933, A097851, A293934, A293935, A293936, A293937, A293938, A293939, A293940, A293941, A293942, A293943 respectively.
Sequence in context: A328337 A285782 A285538 * A285479 A327369 A296620
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2017
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)