A109678 Sequence and first differences include all square numbers exactly once.

1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585

Offset

1,2

Comments

This sequence diverges from A000330 as 4900 (which is 70^2) appears in the sequence itself - thus won't be added to any a(n).

Links

Table of n, a(n) for n=1..42.

Example

Superpose sequence and first differences:
1 5 14 30 55 91 140 204 285 385 506 650 819 1015
.4.9..16..25..36..49...64...81...100...121...144...169...196
All square numbers appear once and only once, either in the sequence itself or in the first differences.

Crossrefs

Sequence in context: A231681 A231685 A074784 * A000330 A266783 A266784

Adjacent sequences: A109675 A109676 A109677 * A109679 A109680 A109681

Keyword

easy,nonn

Author

Eric Angelini, Aug 30 2005

Extensions

Two programs removed that were reproducing A000330 and therefore erroneous. - R. J. Mathar, Mar 06 2013

Status

approved