A265944 Absolute value of the determinant of the matrix whose terms are fibonacci(m+r+s)^(n) with 0 <= r, s <=n, for any m.

1, 2, 36, 13824, 324000000, 1209323520000000, 1923567501916569600000000, 3436011282355888738787131392000000000, 18204541483393435808637499286914987185930240000000000, 753091424970084722185225494963366011108371967508480000000000000000000000

Offset: 1

Author

Michel Marcus, Dec 23 2015

Keywords

• nonn

Links

• L. Carlitz, Some Determinants Containing Powers of Fibonacci Numbers, The Fibonacci Quarterly, 4.2 (1966), 129-134.
• Eric Rowland and Jesus Sistos Barron, Complexity of powers of a constant-recursive sequence, arXiv:2501.14643 [math.NT], 2025. See p. 6.
• Aram Tangboonduangjit and Thotsaporn Thanatipanonda, Determinants Containing Powers of Generalized Fibonacci Numbers, arXiv:1512.07025 [math.CO], 2015.

Crossrefs

Cf. A001142, A152686.

Programs

PARI

a(n) = prod(j=0, n, binomial(n, j)) * prod(j=1,n, fibonacci(j)^(n-j+1))^2;

Formula

a(n) = (Product_{j=0..n} binomial(n,j)) * (Product_{j=1..n} fibonacci(j)^(n-j+1))^2.

a(n) = A001142(n)*A152686(n)^2.