cp's OEIS Frontend

A378716 Triangle read by rows: T(n,k) is the number of k-Fibonacci polyominoes with an area of n, with k > 1.

%I A378716 #10 Dec 06 2024 11:30:50
%S A378716 1,1,1,1,0,1,2,1,0,1,2,2,0,0,1,3,0,1,0,0,1,4,2,1,0,0,0,1,5,3,1,1,0,0,
%T A378716 0,1,7,1,1,1,0,0,0,0,1,9,5,2,0,1,0,0,0,0,1,12,5,1,1,1,0,0,0,0,0,1,16,
%U A378716 3,2,0,0,1,0,0,0,0,0,1,21,10,3,3,0,1,0,0,0,0,0,0,1
%N A378716 Triangle read by rows: T(n,k) is the number of k-Fibonacci polyominoes with an area of n, with k > 1.
%H A378716 Juan F. Pulido, José L. Ramírez, and Andrés R. Vindas-Meléndez, <a href="https://arxiv.org/abs/2411.17812">Generating Trees and Fibonacci Polyominoes</a>, arXiv:2411.17812 [math.CO], 2024. See page 9.
%F A378716 T(n, k) = [x^n] 1/(1 - Sum_{i=1..k} x^((k+i)*(k-i+1)/2) ).
%e A378716 The triangle begins as:
%e A378716    1;
%e A378716    1, 1;
%e A378716    1, 0, 1;
%e A378716    2, 1, 0, 1;
%e A378716    2, 2, 0, 0, 1;
%e A378716    3, 0, 1, 0, 0, 1;
%e A378716    4, 2, 1, 0, 0, 0, 1;
%e A378716    5, 3, 1, 1, 0, 0, 0, 1;
%e A378716    7, 1, 1, 1, 0, 0, 0, 0, 1;
%e A378716    9, 5, 2, 0, 1, 0, 0, 0, 0, 1;
%e A378716   12, 5, 1, 1, 1, 0, 0, 0, 0, 0, 1;
%e A378716   ...
%t A378716 T[n_, k_]:=SeriesCoefficient[1/(1-Sum[x^((k+i)(k-i+1)/2), {i, k}]), {x, 0, n}]; Table[T[n, k], {n, 2, 14}, {k, 2,n}]//Flatten
%Y A378716 Cf. A079957 (k=3), A182097 (k=2), A378704, A378706, A378707.
%K A378716 nonn,tabl
%O A378716 3,7
%A A378716 _Stefano Spezia_, Dec 05 2024