OFFSET
1,2
COMMENTS
See A374848 for the definition of obverse convolution and a guide to related sequences and arrays. If n is odd, then the polynomial u(n) is a square. Every T(n,k) except T(2,1) is even.
EXAMPLE
First 3 polynomials in s(x)**t(x) are
0 + 2x,
1 + 4 x + 4x^2,
2 + 10 x + 16 x^2 + 8 x^3.
First 5 rows of array:
0 2
1 4 4
2 10 16 8
16 64 96 64 16
162 594 864 624 224 32
MATHEMATICA
s[n_] := x + Fibonacci[n]; t[n_] := Fibonacci[n];
u[n_] := Product[s[k] + t[n - k], {k, 0, n}]
Table[Expand[u[n]], {n, 0, 10}]
Column[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]] (* array *)
Flatten[Table[CoefficientList[Expand[u[n]], x], {n, 0, 10}]] (* sequence *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Jul 31 2024
STATUS
approved