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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 Molien series

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]^50, x] (* Jean-Fran├žois 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}, 59]

(* Ray Chandler, Jul 15 2015 *)

CROSSREFS

Cf. A088932 (partial sums), A008804.

Sequence in context: A029009 A023023 A184157 * A008644 A008645 A018819

Adjacent sequences:  A008640 A008641 A008642 * A008644 A008645 A008646

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 19 20:17 EST 2019. Contains 320328 sequences. (Running on oeis4.)