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.

Crossrefs

Cf. A343080, A343085, A343086.

Sequence in context: A008688 A107519 A331641 * A168629 A175521 A214607

Adjacent sequences: A343081 A343082 A343083 * A343085 A343086 A343087

Keyword

nonn

Author

Sean A. Irvine, Apr 04 2021

Status

approved