OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 101 rows, flattened
FORMULA
G.f.: (1 +x*(1+y) +x^2*(2+2*y+y^2) +x^3*y(1+2*y) +2*x^4*y^2)/((1-x^3)*(1-x^3*y^3)).
T(n, k) = [k<=n]*2^abs(L(C(n,2)/3) - L(C(k,2)/3)).
EXAMPLE
Triangle begins
1;
1, 1;
2, 2, 1;
1, 1, 2, 1;
1, 1, 2, 1, 1;
2, 2, 1, 2, 2, 1;
1, 1, 2, 1, 1, 2, 1;
1, 1, 2, 1, 1, 2, 1, 1;
2, 2, 1, 2, 2, 1, 2, 2, 1;
1, 1, 2, 1, 1, 2, 1, 1, 2, 1;
1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1;
2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1;
1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1;
MATHEMATICA
Flatten[CoefficientList[CoefficientList[Series[(1 +x(1+y) +x^2(2+2y+y^2) +x^3*y(1 +2y) +2x^4*y^2)/((1-x^3)(1-x^3*y^3)), {x, 0, 15}, {y, 0, 15}], x], y]] (* G. C. Greubel, May 03 2017 *)
T[n_, k_]:= 2^Abs[JacobiSymbol[Binomial[n, 2], 3] - JacobiSymbol[Binomial[k, 2], 3]]; Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Sep 27 2021 *)
PROG
(Sage)
def T(n, k): return 2^abs(kronecker(binomial(n, 2), 3) - kronecker(binomial(k, 2), 3))
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Sep 27 2021
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 01 2006
STATUS
approved