A395607 a(n) = a(n-1) + a(n-3) + a(n-4), a(0) = 1, a(1) = 6, a(2) = 36, a(3) = 42.

1, 6, 36, 42, 49, 91, 169, 260, 400, 660, 1089, 1749, 2809, 4558, 7396, 11954, 19321, 31275, 50625, 81900, 132496, 214396, 346921, 561317, 908209, 1469526, 2377764, 3847290, 6225025, 10072315, 16297369, 26369684, 42667024, 69036708, 111703761, 180740469, 292444201, 473184670, 765628900

Offset

0,2

Links

Table of n, a(n) for n=0..38.

Tomás Guardia, Douglas Jiménez, and Alexander McCurdy, Fiboquadratic numbers and Rithmomachia, Recreational Mathematics Magazine, Vol. 11, No. 18 (2024), pp. 17-29.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).

Formula

a(n) = (6*F(n/2) + F((n/2)-1))^2 if n is even and (6*F((n-1)/2) + F(((n-1)/2)-1))*(6*F(((n-1)/2)+1) + F((n-1)/2)) if n is odd where F(n) = Fibonacci(n).

G.f.: (1 + 5*x + 30*x^2 + 5*x^3)/((1 + x^2)*(1 - x - x^2)). - Stefano Spezia, Apr 09 2026

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {1, 6, 36, 42}, 40] (* Amiram Eldar, May 03 2026 *)

Crossrefs

Cf. A000045, A006498, A006499.

Sequence in context: A043063 A348384 A328466 * A232137 A008460 A132633

Adjacent sequences: A395604 A395605 A395606 * A395608 A395609 A395610

Keyword

nonn,easy

Author

Alexander McCurdy, Apr 30 2026

Status

approved