A248928 Interleave (2*n+2)^2 with (2*n+3)^2, both listed n+1 times.

4, 9, 16, 16, 25, 25, 36, 36, 36, 49, 49, 49, 64, 64, 64, 64, 81, 81, 81, 81, 100, 100, 100, 100, 100, 121, 121, 121, 121, 121, 144, 144, 144, 144, 144, 144, 169, 169, 169, 169, 169, 169, 196, 196, 196, 196, 196, 196, 196, 225, 225, 225, 225, 225, 225, 225

Offset

0,1

Comments

Discovered via Janet's sequence A167268: the result of adding to A167268 the smallest increasing sequence (2, 7, 10, 14, 19, 23, 26, 30, 34, 39, 43, 47, ...) as to get a sequence of nondecreasing squares.

Even terms: 4, 16, 16, 36, 36, 36, ... = 4*A093995(n+1).

Odd terms: (A131507(n) + 2)^2.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = A027434(n+1)^2.

Example

Seen as an irregular triangle:
4;
9;
16, 16;
25, 25;
36, 36, 36;
49, 49, 49;
64, 64, 64, 64;
81, 81, 81, 81;
...

Mathematica

Module[{nn=10, a, b}, a=Table[PadRight[{}, n+1, (2n+2)^2], {n, 0, nn}]; b= Table[ PadRight[ {}, n+1, (2n+3)^2], {n, 0, nn}]; Riffle[a, b]]//Flatten (* Harvey P. Dale, Jun 10 2022 *)

Prog

(PARI) vector(60, n, (sqrtint(4*n-3)+1)^2) \\ after Charles R Greathouse IV, Michel Marcus, Oct 27 2014

Crossrefs

Cf. A000267, A007395, A027434, A093995, A131507, A167268.

Sequence in context: A313306 A313307 A313308 * A080819 A313309 A313310

Adjacent sequences: A248925 A248926 A248927 * A248929 A248930 A248931

Keyword

nonn,tabf

Author

Paul Curtz, Oct 17 2014

Status

approved