A381503 Number of rectangles in a Fibonacci(n) X Fibonacci(n+1) grid.

1, 3, 18, 90, 540, 3276, 21021, 137445, 916300, 6167700, 41812200, 284604840, 1942428033, 13278352815, 90862598190, 622150990734, 4261620339460, 29198279495220, 200080147593645, 1371167039301345, 9397260307853496, 64406143791454248, 441430873666787088, 3025546968019741200

Offset: 1

Author

Darío Clavijo, Feb 25 2025

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A033192, A096948, A377704.

Programs

Mathematica

Times @@@ Partition[PolygonalNumber[Fibonacci[Range[25]]], 2, 1] (* Paolo Xausa, Mar 13 2025 *)

Python

from sympy import fibonacci
A096948 = lambda n,m: (m * (m + 1) * n * (n + 1)) >> 2
a = lambda n: A096948(fibonacci(n),fibonacci(n+1))
print([a(n) for n in range(1, 25)])

Formula

a(n) = A096948(Fibonacci(n),Fibonacci(n+1)).

a(n) = A033192(n) * A033192(n+1).