A343084 a(n) is the smallest number that is the sum of n positive squares in four ways.

1105, 129, 52, 53, 36, 37, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89

Offset: 2

Author

Sean A. Irvine, Apr 04 2021

Keywords

• nonn

Comments

This is r(n,2,4) in Alter's notation.

Examples

			a(2) = 1105 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2 = 23^2 + 24^2.
a(3) = 129 = 1^2 + 8^2 + 8^2 = 2^2 + 2^2 + 11^2 = 2^2 + 5^2 + 10^2 = 4^2 + 7^2 + 8^2.
		

Links

• R. Alter, Computations and generalizations on a remark of Ramanujan, pp. 182-196 of "Analytic Number Theory (Philadelphia, 1980)", ed. M. I. Knopp, Lect. Notes Math., Vol. 899, 1981. See Table 10, page 193.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A343080, A343085, A343086.

Programs

Mathematica

LinearRecurrence[{2,-1},{1105,129,52,53,36,37,32,33},70] (* Harvey P. Dale, Mar 18 2025 *)

Formula

a(n) = n + 24 for n >= 8.