A109593 Sequence and first differences include all odd numbers exactly once.

1, 4, 9, 16, 27, 40, 55, 72, 91, 112, 135, 160, 189, 220, 253, 288, 325, 364, 405, 448, 493, 540, 589, 640, 693, 750, 809, 870, 933, 998, 1065, 1134, 1205, 1278, 1353, 1430, 1509, 1590, 1673, 1758, 1845, 1934, 2027, 2122, 2219, 2318, 2419, 2522, 2627, 2734

Offset

1,2

Comments

See A005228.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = n^2 + C*n^(3/2) + O(n), where C = 5/6. According to the simplified model: the sum of n consecutive odd numbers without the odd squares. - Thomas Ordowski, Sep 24 2014

Mathematica

a = {1}; d = 3; k = 1; Do[ While[ Position[a, d] != {}, d += 2 ]; k = k + d; d += 2; a = Append[a, k], {n, 49} ]; a (* Robert G. Wilson v, Sep 28 2005 *)

Crossrefs

Cf. A005228.

Sequence in context: A195618 A066969 A213495 * A237589 A138981 A138993

Adjacent sequences: A109590 A109591 A109592 * A109594 A109595 A109596

Keyword

base,easy,nonn

Author

Eric Angelini, Aug 30 2005

Extensions

Corrected and extended by Robert G. Wilson v, Sep 28 2005

Status

approved