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!)
 A008643 Molien series for group of 4 X 4 upper triangular matrices over GF(2). 3
 1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26, 26, 35, 35, 44, 44, 56, 56, 68, 68, 84, 84, 100, 100, 120, 120, 140, 140, 165, 165, 190, 190, 220, 220, 250, 250, 286, 286, 322, 322, 364, 364, 406, 406, 455, 455, 504, 504, 560, 560, 616, 616, 680, 680, 744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of partitions of n into parts 1, 2, 4 and 8. - Ilya Gutkovskiy, May 24 2017 REFERENCES D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 233 Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1). FORMULA G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)). a(n) = floor(((n+14)*(3*(n+1)*(-1)^n + 2*n^2 + 17*n + 57) + 24*(floor(n/2) + 1)*(-1)^floor(n/2))/768). - Tani Akinari, Jun 16 2013 a(n) ~ 1/384*n^3. - Ralf Stephan, Apr 29 2014 MAPLE a:= proc(n) local m, r; m := iquo(n, 8, 'r'); r:= iquo(r, 2)+1; ([11, 17, 26, 35][r]+ (9+ 3*r+ 4*m) *m) *m/3+ [1, 2, 4, 6][r] end: seq(a(n), n=0..100);  # Alois P. Heinz, Oct 06 2008 MATHEMATICA CoefficientList[1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)) + O[x]^65, x] (* Jean-François Alcover, May 29 2015 *) LinearRecurrence[{1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1}, {1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, 26}, 65] (* Ray Chandler, Jul 15 2015 *) PROG (PARI) my(x='x+O('x^65)); Vec(1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8))) \\ G. C. Greubel, Feb 01 2020 (MAGMA) R:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (&*[1/(1-x^(2^j)): j in [0..3]]) )); // G. C. Greubel, Feb 01 2020 (Sage) def A077952_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^8)) ).list() A077952_list(65) # G. C. Greubel, Feb 01 2020 CROSSREFS Cf. A008804, A088932 (partial sums). Sequence in context: A343100 A023023 A184157 * A008644 A008645 A018819 Adjacent sequences:  A008640 A008641 A008642 * A008644 A008645 A008646 KEYWORD nonn,easy AUTHOR 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 May 12 06:44 EDT 2021. Contains 343820 sequences. (Running on oeis4.)