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

Table of n, a(n) for n=1..50.

Index entries for linear recurrences with constant coefficients, signature (2, 0, -2, 1).

Formula

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

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). - R. J. Mathar, Oct 24 2008

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.

Crossrefs

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