A388539 Sum of decimal digits of Fibonacci(n)^2.

0, 1, 1, 4, 9, 7, 10, 16, 9, 13, 10, 19, 18, 28, 19, 13, 36, 25, 37, 34, 36, 40, 37, 37, 45, 46, 46, 40, 27, 43, 46, 34, 54, 49, 55, 46, 54, 55, 82, 49, 72, 88, 64, 106, 90, 67, 73, 73, 81, 91, 100, 85, 99, 97, 127, 106, 81, 94, 100, 100, 90, 91, 109, 121, 108

Offset

0,4

Links

Saeed Hatami Boura, Table of n, a(n) for n = 0..10000

Formula

a(n) = A007953(A007598(n)).

Example

a(7) = 16 because F(7) = 13, 13^2 = 169, and 1 + 6 + 9 = 16.

Maple

seq(convert(convert(combinat:-fibonacci(n)^2, base, 10), `+`), n=0..100); # Robert Israel, Sep 19 2025

Mathematica

a[n_] := DigitSum[Fibonacci[n]^2]; Array[a, 100, 0] (* Amiram Eldar, Sep 18 2025 *)

Prog

(Python)
def a(n):
    f0, f1 = 0, 1
    for _ in range(n):
        f0, f1 = f1, f0 + f1
    return sum(int(d) for d in str(f0 * f0))
(PARI) a(n) = sumdigits(fibonacci(n)^2); \\ Michel Marcus, Sep 19 2025

Crossrefs

Cf. A007598 (squared Fibonacci numbers), A007953 (digital sum), A216676.

Sequence in context: A155787 A338304 A179222 * A123157 A154684 A353071

Adjacent sequences: A388536 A388537 A388538 * A388540 A388541 A388542

Keyword

nonn,base

Author

Saeed Hatami Boura, Sep 18 2025

Status

approved