A378254 Cogrowth sequence of the 20-element group C10 X C2 = <S,T | S^10, T^2, [S,T]>.

1, 1, 1, 1, 1, 2, 67, 1002, 8009, 43759, 184758, 646878, 1971883, 5541966, 16231216, 60090032, 290305577, 1523150157, 7564006759, 34099637859, 139541849878, 526321168143, 1878476551128, 6603812572941, 24052434515891, 94278969044262, 396750746960712

Offset

0,6

Comments

Gives the even terms, all the odd terms are 0.

Links

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

Formula

G.f.: (10*x^9+75*x^8+162*x^7-48*x^6+127*x^5-126*x^4+84*x^3-36*x^2+9*x-1) / ((4*x-1) * (25*x^4+10*x^2-5*x+1) * (x^4+4*x^3+6*x^2-x+1)).

Mathematica

CoefficientList[Series[(10*x^9+75*x^8+162*x^7-48*x^6+127*x^5-126*x^4+84*x^3-36*x^2+9*x-1)/((4*x-1)*(25*x^4+10*x^2-5*x+1)*(x^4+4*x^3+6*x^2-x+1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 10 2025 *)

Prog

(Magma) m:=35; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((10*x^9+75*x^8+162*x^7-48*x^6+127*x^5-126*x^4+84*x^3-36*x^2+9*x-1) / ((4*x-1) * (25*x^4+10*x^2-5*x+1) * (x^4+4*x^3+6*x^2-x+1)))); // Vincenzo Librandi, Oct 10 2025

Crossrefs

Cf. A377840 (C8 X C2), A377627 (C6 X C2), A078789 (D10).

Sequence in context: A046848 A318064 A089661 * A355326 A191808 A364069

Adjacent sequences: A378251 A378252 A378253 * A378255 A378256 A378257

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 20 2024

Status

approved