A024163 Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b < b - a.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 3, 3, 6, 3, 6, 6, 6, 6, 10, 6, 10, 10, 10, 10, 15, 10, 15, 15, 15, 15, 21, 15, 21, 21, 21, 21, 28, 21, 28, 28, 28, 28, 36, 28, 36, 36, 36, 36, 45, 36, 45, 45, 45, 45, 55, 45, 55, 55, 55, 55, 66, 55, 66, 66, 66, 66, 78, 66, 78, 78, 78, 78, 91

Offset

1,17

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x^11/((1-x^2)*(1-x^3)*(1-x^6)). - Tani Akinari, Oct 27 2014

Example

2,4,5 for n=11 is the smallest such triangle.

Mathematica

CoefficientList[Series[x^10/((1-x^2)(1-x^3)(1-x^6)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 28 2014 *)

Prog

(PARI) concat(vector(11, i, 0), Vec(1/(1-x^2)/(1-x^3)/(1-x^6)+O(x^99))) \\ Charles R Greathouse IV, Oct 28 2014
(Sage)
def A024163_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( x^11/((1-x^2)*(1-x^3)*(1-x^6)) ).list()
a=A024163_list(100); a[1:] # G. C. Greubel, Jul 03 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 100);
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] cat Coefficients(R!( x^11/((1-x^2)*(1-x^3)*(1-x^6)) )); // G. C. Greubel, Jul 03 2021

Crossrefs

Cf. A024165.

Sequence in context: A063195 A334070 A025796 * A029155 A042951 A194299

Adjacent sequences: A024160 A024161 A024162 * A024164 A024165 A024166

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved