A114002 - OEIS

%I #10 Sep 08 2023 12:01:42

%S 1,2,1,2,0,1,2,2,0,1,2,0,0,0,1,2,2,2,0,0,1,2,0,0,0,0,0,1,2,2,0,2,0,0,

%T 0,1,2,0,2,0,0,0,0,0,1,2,2,0,0,2,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,1,2,2,

%U 2,2,0,2,0,0,0,0,0,1,2,0,0,0,0,0,0,0,0,0,0,0,1,2,2,0,0,0,0,2,0,0,0,0,0,0,1

%N Expansion of g.f. x^k(1+x^(k+1))/(1-x^(k+1)).

%C Inverse is A114004. Row sums are A114003.

%F Column k has g.f. x^k(1+x^(k+1))/(1-x^(k+1)).

%F Equals 2*A051731 - I, I = Identity matrix. - _Gary W. Adamson_, Nov 07 2007

%e Triangle begins:

%e   1;

%e   2, 1;

%e   2, 0, 1;

%e   2, 2, 0, 1;

%e   2, 0, 0, 0, 1;

%e   2, 2, 2, 0, 0, 1;

%e   2, 0, 0, 0, 0, 0, 1;

%e   ...

%t T[n_,k_]:=SeriesCoefficient[x^k(1+x^(k+1))/(1-x^(k+1)),{x,0,n}]; Table[T[n,k],{n,0,13},{k,0,n}] //Flatten (* _Stefano Spezia_, Sep 08 2023 *)

%Y Cf. A051731, A114003, A114004.

%K easy,nonn,tabl

%O 0,2

%A _Paul Barry_, Nov 12 2005