A395266 - OEIS

A395266

a(n) = a(n-1) + a(n-3) + a(n-4), a(0) = 1, a(1) = 5, a(2) = 25, a(3) = 30.

1, 5, 25, 30, 36, 66, 121, 187, 289, 476, 784, 1260, 2025, 3285, 5329, 8614, 13924, 22538, 36481, 59019, 95481, 154500, 250000, 404500, 654481, 1058981, 1713481, 2772462, 4485924, 7258386, 11744329, 19002715, 30747025, 49749740, 80496784, 130246524, 210743289

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..36.

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) = (5*F(n/2) + F((n/2)-1))^2 if n is even and (5*F((n-1)/2) + F(((n-1)/2)-1))*(5*F(((n-1)/2)+1) + F((n-1)/2)) if n is odd where F(n) = Fibonacci(n).

G.f.: (1 + 4*x + 20*x^2 + 4*x^3)/((1 + x^2)*(1 - x - x^2)). - Stefano Spezia, Apr 09 2026

MATHEMATICA

LinearRecurrence[{1, 0, 1, 1}, {1, 5, 25, 30}, 37] (* Amiram Eldar, Apr 18 2026 *)

CROSSREFS

Cf. A000045, A006498, A006499.

Sequence in context: A000350 A000221 A018612 * A036127 A291755 A018639

Adjacent sequences: A395263 A395264 A395265 * A395267 A395268 A395269

KEYWORD

nonn,easy

AUTHOR

Alexander McCurdy, Apr 17 2026

STATUS

approved