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A061866 a(n) is the number of solutions to x+y+z = 0 mod 3, where 1 <= x < y < z <= n. 4
0, 0, 0, 1, 2, 4, 8, 13, 20, 30, 42, 57, 76, 98, 124, 155, 190, 230, 276, 327, 384, 448, 518, 595, 680, 772, 872, 981, 1098, 1224, 1360, 1505, 1660, 1826, 2002, 2189, 2388, 2598, 2820, 3055, 3302, 3562, 3836, 4123, 4424, 4740, 5070, 5415, 5776, 6152, 6544, 6953, 7378, 7820 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
(1+x)*(1+x^2)*(1+x^3) / ( (1-x)*(1-x^2)*(1-x^3)*(1-x^4)) is the Poincaré series [or Poincare series] (or Molien series) for H^*(O_4(q); F_2).
REFERENCES
A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 233.
LINKS
D. Z. Dokovic, B. H. Smith, Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities, Lin. Alg. Applic. 428 (4) (2008) 890-910
FORMULA
G.f.: x^3*(1+x)*(1+x^2)*(1+x^3) / ( (1-x)*(1-x^2)*(1-x^3)*(1-x^4)). - N. J. A. Sloane, Mar 17 2004
a(n) = (binomial(n,3)+2*floor(n/3))/3. - Claude Morin, Mar 06 2012
G.f.: x^3*(1-x+x^2) / ( (1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Dec 18 2014
a(n+5) = A014125(n)-A014125(n+1)+A014125(n+2). - R. J. Mathar, Mar 11 2019
MATHEMATICA
LinearRecurrence[{3, -3, 2, -3, 3, -1}, {0, 0, 0, 1, 2, 4}, 60] (* Harvey P. Dale, Nov 22 2014 *)
CROSSREFS
The third diagonal of A061865.
Sequence in context: A359850 A349216 A247587 * A164476 A164466 A164487
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, May 11 2001
STATUS
approved

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Last modified May 26 02:25 EDT 2024. Contains 372807 sequences. (Running on oeis4.)