A298802 Growth series for group with presentation < S, T : S^4 = T^4 = (S*T)^4 = 1 >.

1, 4, 10, 24, 56, 128, 294, 676, 1552, 3564, 8186, 18800, 43176, 99160, 227734, 523020, 1201184, 2758676, 6335658, 14550664, 33417496, 76747632, 176260934, 404806196, 929690160, 2135154556, 4903660570, 11261895264, 25864409480, 59400985544, 136422101046, 313311125788, 719559813184

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,2,-1).

Formula

G.f.: (1 + x)^2*(1 + x^2) / (1 - 2*x - 2*x^3 + x^4).

a(n) = 2*a(n-1) + 2*a(n-3) - a(n-4) for n>4. - Colin Barker, Feb 04 2018

Mathematica

LinearRecurrence[{2, 0, 2, -1}, {1, 4, 10, 24, 56}, 40] (* Harvey P. Dale, Jan 02 2020 *)

Prog

(Magma)
R<x> := RationalFunctionField(Integers());
PSR25 := PowerSeriesRing(Integers():Precision := 25);
FG<S, T> := FreeGroup(2);
TG := quo<FG | S^4, T^4, (S*T)^4 >;
f, A :=IsAutomaticGroup(TG);
gf := GrowthFunction(A);
R!gf;
Coefficients(PSR25!gf);
(PARI) Vec((1 + x)^2*(1 + x^2) / (1 - 2*x - 2*x^3 + x^4) + O(x^40)) \\ Colin Barker, Feb 04 2018

Crossrefs

Cf. A008579.

Sequence in context: A087447 A129953 A079859 * A118871 A019494 A192886

Adjacent sequences: A298799 A298800 A298801 * A298803 A298804 A298805

Keyword

nonn,easy

Author

John Cannon and N. J. A. Sloane, Feb 04 2018

Status

approved