A378276 Cogrowth sequence of the 20-element dicyclic group Dic20 = <S,T | S^5, T^4, STST^3>.

1, 0, 0, 0, 1, 0, 6, 7, 19, 9, 61, 88, 226, 377, 945, 1473, 3427, 6154, 13758, 25327, 53967, 102865, 213345, 411700, 849706, 1661885, 3382821, 6668577, 13493719, 26725414, 53861446, 107074403, 215261971, 428704177, 860266725, 1715950208, 3439229842, 6866462849

Offset

0,7

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: (4*x^9-6*x^8-3*x^7-5*x^6-2*x^5-2*x^4-2*x^3-x^2+1) / ((2*x-1) * (2*x^2+2*x+1) * (x^2-x-1) * (4*x^4-2*x^3+3*x^2-x+1)).

Mathematica

CoefficientList[Series[(4*x^9-6*x^8-3*x^7-5*x^6-2*x^5-2*x^4-2*x^3-x^2+1)/((2*x-1)*(2*x^2+2*x+1)*(x^2-x-1)*(4*x^4-2*x^3+3*x^2-x+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 10 2025 *)

Prog

(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((4*x^9-6*x^8-3*x^7-5*x^6-2*x^5-2*x^4-2*x^3-x^2+1) / ((2*x-1) * (2*x^2+2*x+1) * (x^2-x-1) * (4*x^4-2*x^3+3*x^2-x+1)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

Cf. A377656 (Dic12), A078789 (D10), A378254 (C10 X C2), A378278 (Frob20).

Sequence in context: A005302 A367599 A028324 * A074342 A329072 A102789

Adjacent sequences: A378273 A378274 A378275 * A378277 A378278 A378279

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 21 2024

Status

approved