A024163
Number of integer-sided triangles with sides a,b,c, 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
Examples
2,4,5 for n=11 is the smallest such triangle.
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).
Programs
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Magma
R
:=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 -
Mathematica
CoefficientList[Series[x^10/((1-x^2)(1-x^3)(1-x^6)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 28 2014 *) -
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
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Sage
def A024163_list(prec): P.
= 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
Formula
G.f.: x^11/((1-x^2)*(1-x^3)*(1-x^6)). - Tani Akinari, Oct 27 2014
Comments