A394245 a(n) = a(n-1) + a(n-3) + a(n-4), a(0) = 1, a(1) = 10, a(2) = 100, a(3) = 110.

1, 10, 100, 110, 121, 231, 441, 672, 1024, 1696, 2809, 4505, 7225, 11730, 19044, 30774, 49729, 80503, 130321, 210824, 341056, 551880, 893025, 1444905, 2337841, 3782746, 6120676, 9903422, 16024009, 25927431, 41951529, 67878960, 109830400, 177709360, 287539849, 465249209, 752788969, 1218038178, 1970827236

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) = (10*F(n/2) + F((n/2)-1))^2 if n is even and (10*F((n-1)/2) + F(((n-1)/2)-1))*(10*F(((n-1)/2)+1) + F((n-1)/2)) if n is odd where F(n) = Fibonacci(n).

G.f.: (1 + 9*x + 90*x^2 + 9*x^3)/(1 - x - x^3 - x^4). \\ Hoang Xuan Thanh, May 15 2026

Mathematica

LinearRecurrence[{1, 0, 1, 1}, {1, 10, 100, 110}, 40] (* Amiram Eldar, May 15 2026 *)

Prog

(PARI) Vec((1 + 9*x + 90*x^2 + 9*x^3)/(1 - x - x^3 - x^4) + O(x^40)) \\ Hoang Xuan Thanh, May 15 2026

Crossrefs

Cf. A000045, A006498, A006499.

Sequence in context: A174417 A169666 A169662 * A124252 A121030 A327786

Adjacent sequences: A394242 A394243 A394244 * A394246 A394247 A394248

Keyword

nonn,easy

Author

Alexander McCurdy, May 14 2026

Status

approved