A142717 First (leftmost) odd term in the n-th row of triangle A120070.

3, 5, 15, 21, 35, 45, 63, 77, 99, 117, 143, 165, 195, 221, 255, 285, 323, 357, 399, 437, 483, 525, 575, 621, 675, 725, 783, 837, 899, 957, 1023, 1085, 1155, 1221, 1295, 1365, 1443, 1517, 1599, 1677, 1763, 1845, 1935, 2021, 2115, 2205, 2303, 2397, 2499, 2597

Offset: 1

Author

Paul Curtz, Sep 26 2008

Keywords

• nonn

Comments

Also: Records sequence of A100181.

The last (rightmost) term in the n-th row of triangle A120070 is A005408(n).

Examples

			The odd terms of A120070 build the irregular triangle
  3;
  5;
  15,7;
  21,9;
  35,27,11;
  45,33,13;
  63,55,39,15;
The leftmost column defines this sequence.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A000466, A078371, A100181.

Programs

Mathematica

A142717[n_]:=(n+1)^2-If[OddQ[n],1,4];Array[A142717,100] (* or *)
LinearRecurrence[{2,0,-2,1},{3,5,15,21},100] (* Paolo Xausa, Dec 05 2023 *)

Formula

First differences: a(n+1)-a(n) = A142954(n).

From R. J. Mathar, Oct 24 2008: (Start)

a(n) = (n+1)^2-1 = A000466((n+1)/2) if n odd.

a(n) = (n+1)^2-4 = A078371(n/2-1) if n even.

a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).

G.f.: x(3-x+5x^2-3x^3)/((1+x)(1-x)^3). (End)

Extensions

Edited and extended by R. J. Mathar, Oct 24 2008