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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A293933 Poincare series for invariant polynomial functions on the space of binary forms of degree 7. 13
 1, 0, 1, 0, 4, 0, 10, 4, 18, 13, 35, 26, 62, 52, 97, 92, 153, 144, 229, 223, 325, 329, 456, 460, 624, 636, 826, 856, 1084, 1119, 1398, 1449, 1766, 1845, 2214, 2306, 2743, 2860, 3349, 3507, 4065, 4245, 4889, 5107, 5820, 6093, 6893, 7200, 8108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Many of these Poincare series has every other term zero, in which case these zeros have been omitted. LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Andries Brouwer, Poincaré Series (See n=7) FORMULA a(n) = (11/8640)*n^4 + (11/1080)*n^3 + O(n^2). - Robert Israel, Oct 20 2017 EXAMPLE The Poincare series is (1 - t^6 + 2t^8 - t^10 + 5t^12 + 2t^14 + 6t^16 + 2t^18 + 5t^20 - t^22 + 2t^24 - t^26 + t^32) / (1 - t^4)(1 - t^6)(1 - t^8)(1 - t^10)(1 - t^12) MAPLE (x^16-x^13+2*x^12-x^11+5*x^10+2*x^9+6*x^8+2*x^7+5*x^6-x^5+2*x^4-x^3+1)/(-x^2+1)/(-x^3+1)/(-x^4+1)/(-x^5+1)/(-x^6+1); f := gfun:-rectoproc({-12*a(n) - 60*a(n+1) - 168*a(n+2) - 348*a(n+3) - 588*a(n+4) - 852*a(n+5) - 1080*a(n+6) - 1212*a(n+7) - 1212*a(n+8) - 1080*a(n+9) - 852*a(n+10) - 588*a(n+11) - 348*a(n+12) - 168*a(n+13) - 60*a(n+14) - 12*a(n+15) + 11*n^4 + 418*n^3 + 6433*n^2 + 46778*n + 136380, a(0) = 1, a(1) = 0, a(2) = 1, a(3) = 0, a(4) = 4, a(5) = 0, a(6) = 10, a(7) = 4, a(8) = 18, a(9) = 13, a(10) = 35, a(11) = 26, a(12) = 62, a(13) = 52, a(14) = 97, a(15) = 92, a(16) = 153}, a(n), remember): map(f, [\$0..100]); # Robert Israel, Oct 20 2017 MATHEMATICA a = DifferenceRoot[Function[{a, n}, {-60*a[n + 1] - 168*a[n + 2] - 348*a[n + 3] - 588*a[n + 4] - 852*a[n + 5] - 1080*a[n + 6] - 1212*a[n + 7] - 1212*a[n + 8] - 1080*a[n + 9] - 852*a[n + 10] - 588*a[n + 11] - 348*a[n + 12] - 168*a[n + 13] - 60*a[n + 14] - 12*a[n + 15] - 12*a[n] + 11*n^4 + 418*n^3 + 6433*n^2 + 46778*n + 136380 == 0, a[0] == 1, a[1] == 0, a[2] == 1, a[3] == 0, a[4] == 4, a[5] == 0, a[6] == 10, a[7] == 4, a[8] == 18, a[9] == 13, a[10] == 35, a[11] == 26, a[12] == 62, a[13] == 52, a[14] == 97}]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 04 2019, after Robert Israel *) CROSSREFS For these Poincare 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: A184363 A331451 A164735 * A158976 A211243 A181626 Adjacent sequences:  A293930 A293931 A293932 * A293934 A293935 A293936 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 17 18:14 EST 2020. Contains 332005 sequences. (Running on oeis4.)