cp's OEIS Frontend

A099233 Square array read by antidiagonals associated to sections of 1/(1-x-x^k).

%I A099233 #19 Mar 26 2023 10:25:36
%S A099233 1,1,1,1,1,1,1,1,2,1,1,1,3,3,1,1,1,4,6,5,1,1,1,5,10,13,8,1,1,1,6,15,
%T A099233 26,28,13,1,1,1,7,21,45,69,60,21,1,1,1,8,28,71,140,181,129,34,1,1,1,9,
%U A099233 36,105,251,431,476,277,55,1,1,1,10,45,148,413,882,1326,1252,595,89,1
%N A099233 Square array read by antidiagonals associated to sections of 1/(1-x-x^k).
%H A099233 Seiichi Manyama, <a href="/A099233/b099233.txt">Antidiagonals n = 0..139, flattened</a>
%F A099233 Square array T(n, k) = Sum_{j=0..n} binomial(k(n-j), j).
%F A099233 Rows are generated by 1/(1-x(1+x)^k) and satisfy a(n) = Sum_{k=0..n} binomial(n, k)a(n-k-1).
%e A099233 Rows begin
%e A099233   1, 1, 1,  1,  1,   1, ...
%e A099233   1, 1, 2,  3,  5,   8, ...
%e A099233   1, 1, 3,  6, 13,  28, ...
%e A099233   1, 1, 4, 10, 26,  69, ...
%e A099233   1, 1, 5, 15, 45, 140, ...
%e A099233 Row 1 is the 0-section of 1/(1-x-x)   (A000079);
%e A099233 Row 2 is the 1-section of 1/(1-x-x^2) (A000045);
%e A099233 Row 3 is the 2-section of 1/(1-x-x^3) (A000930);
%e A099233 Row 4 is the 3-section of 1/(1-x-x^4) (A003269);
%e A099233 etc.
%Y A099233 Sums of antidiagonals are A099236.
%Y A099233 Columns include A000217, A008778.
%Y A099233 Rows include A000045, A002478, A099234, A099235.
%Y A099233 Main diagonal gives A099237.
%Y A099233 Cf. A099238.
%K A099233 easy,nonn,tabl
%O A099233 0,9
%A A099233 _Paul Barry_, Oct 08 2004