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

1,1

Comments

Also: Records sequence of A100181.

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

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).

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)

Example

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.

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 *)

Crossrefs

Cf. A000466, A078371, A100181.

Sequence in context: A201874 A059528 A070079 * A057742 A201433 A101129

Adjacent sequences: A142714 A142715 A142716 * A142718 A142719 A142720

Keyword

nonn

Author

Paul Curtz, Sep 26 2008

Extensions

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

Status

approved