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

2,1

Comments

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

Links

Table of n, a(n) for n=2..65.

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).

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) a(n)=if(n>7, n+24, [1105, 129, 52, 53, 36, 37][n-1]) \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A343080, A343085, A343086.

Sequence in context: A008688 A107519 A331641 * A168629 A175521 A214607

Adjacent sequences: A343081 A343082 A343083 * A343085 A343086 A343087

Keyword

nonn,easy

Author

Sean A. Irvine, Apr 04 2021

Status

approved