|
|
A024165
|
|
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b > b - a.
|
|
2
|
|
|
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 2, 2, 1, 4, 2, 2, 4, 4, 2, 6, 4, 4, 6, 6, 4, 9, 6, 6, 9, 9, 6, 12, 9, 9, 12, 12, 9, 16, 12, 12, 16, 16, 12, 20, 16, 16, 20, 20, 16, 25, 20, 20, 25, 25, 20, 30, 25, 25, 30, 30, 25, 36, 30, 30, 36, 36, 30, 42, 36, 36, 42, 42, 36, 49, 42, 42, 49, 49
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,19
|
|
COMMENTS
|
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,1,1,0,1,-1,0,-1,-1,0,0,1).
|
|
FORMULA
|
G.f.: x^13/((1-x^3)*(1-x^4)*(1-x^6)). - Tani Akinari, Nov 04 2014
a(n) = a(n-3) + a(n-4) + a(n-6) - a(n-7) - a(n-9) - a(n-10) + a(n-13) for n >= 14.
a(6*n) = (2*n^2 - 8*n + 7 + (-1)^n)/8, n >= 1.
a(6*n+1) = a(6*n+4) = a(6*n+5) = (2*n^2 - 1 + (-1)^n)/8.
a(6*n+2) = a(6*n+3) = (2*n^2 - 4*n + 1 - (-1)^n)/8.
(End)
|
|
MATHEMATICA
|
LinearRecurrence[{0, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, 100] (* Harvey P. Dale, Sep 04 2017 *)
|
|
PROG
|
(Sage)
P.<x> = PowerSeriesRing(QQ, prec)
return P( x^13/((1-x^3)*(1-x^4)*(1-x^6)) ).list()
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 100);
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] cat Coefficients(R!( x^13/((1-x^3)*(1-x^4)*(1-x^6)) )); // G. C. Greubel, Jul 03 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|