OFFSET
0,2
COMMENTS
This is associated with the root system E7, and can be described using the additive function on the affine E7 diagram:
2
|
1--2--3--4--3--2--1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 2, -4, -3, 0, 7, 4, -5, -4, -5, 4, 7, 0, -3, -4, 2, 2, -1).
FORMULA
G.f.: 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)).
MAPLE
seq(coeff(series(1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)), x, n+1), x, n), n = 0 .. 40); # G. C. Greubel, Jan 13 2020
MATHEMATICA
CoefficientList[Series[1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)), {x, 0, 40}], x] (* G. C. Greubel, Jan 13 2020 *)
LinearRecurrence[{2, 2, -4, -3, 0, 7, 4, -5, -4, -5, 4, 7, 0, -3, -4, 2, 2, -1}, {1, 2, 6, 12, 25, 44, 79, 128, 208, 318, 483, 704, 1019, 1430, 1992, 2712, 3664, 4862}, 40] (* Harvey P. Dale, Sep 24 2021 *)
PROG
(Sage)
x=PowerSeriesRing(QQ, 'x', 40).gen()
1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4))
(PARI) Vec(1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4))+O(x^40)) \\ Charles R Greathouse IV, Sep 26 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1-x)^2*(1-x^2)^3*(1-x^3)^2*(1-x^4)) )); // G. C. Greubel, Jan 13 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, Mar 17 2012
STATUS
approved