A111802 n^2-n-1 for n>3; a(1)=1; a(2)=2; a(3)=3.

1, 2, 3, 11, 19, 29, 41, 55, 71, 89, 109, 131, 155, 181, 209, 239, 271, 305, 341, 379, 419, 461, 505, 551, 599, 649, 701, 755, 811, 869, 929, 991, 1055, 1121, 1189, 1259, 1331, 1405, 1481, 1559, 1639, 1721, 1805, 1891, 1979, 2069, 2161, 2255, 2351, 2449, 2549

Offset

1,2

Comments

Inspired by attempt to determine what incorrectly-named A000519 may really be. Conjecture: Sequence is number of different main-diagonal sums among Latin squares of order n. Confirmed for first five terms. Guaranteed to be an upper bound as the diagonal sum can only be in the range from n to n^2 inclusive and it is impossible for the sum to be n+1 or n^2-1. There is probably an easy proof that all other sums in this interval can be realized as the only restriction seems to be that it is not permissible for exactly n-1 numbers on a diagonal to be identical.

Links

Table of n, a(n) for n=1..51.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = n^2-n-1 = A028387(n-2) for n>3; a(n) = n for 1<=n<=3.

Example

a(3) = 3, the number of different diagonal sums of all order 3 Latin squares. Their diagonal sums can only be 3, 6 and 9.

Mathematica

Table[If[n<4, n, n^2-n-1], {n, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 3, 11, 19, 29}, 60] (* Harvey P. Dale, Sep 04 2018 *)

Prog

(PARI) a(n)=if(n>3, n^2-n-1, n) \\ Charles R Greathouse IV, Dec 20 2011

Crossrefs

Cf. A028387.

Sequence in context: A135206 A368278 A235629 * A213894 A294668 A095282

Adjacent sequences: A111799 A111800 A111801 * A111803 A111804 A111805

Keyword

nonn,easy

Author

Rick L. Shepherd, Aug 17 2005

Status

approved