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A142717
First (leftmost) odd term in the n-th row of triangle A120070.
5
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).
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
KEYWORD
nonn
AUTHOR
Paul Curtz, Sep 26 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Oct 24 2008
STATUS
approved