|
%I #15 Dec 05 2023 09:22:14
%S 3,5,15,21,35,45,63,77,99,117,143,165,195,221,255,285,323,357,399,437,
%T 483,525,575,621,675,725,783,837,899,957,1023,1085,1155,1221,1295,
%U 1365,1443,1517,1599,1677,1763,1845,1935,2021,2115,2205,2303,2397,2499,2597
%N First (leftmost) odd term in the n-th row of triangle A120070.
%C Also: Records sequence of A100181.
%C The last (rightmost) term in the n-th row of triangle A120070 is A005408(n).
%H Paolo Xausa, <a href="/A142717/b142717.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F First differences: a(n+1)-a(n) = A142954(n).
%F From _R. J. Mathar_, Oct 24 2008: (Start)
%F a(n) = (n+1)^2-1 = A000466((n+1)/2) if n odd.
%F a(n) = (n+1)^2-4 = A078371(n/2-1) if n even.
%F a(n) = 2*a(n-1) -2*a(n-3) +a(n-4).
%F G.f.: x(3-x+5x^2-3x^3)/((1+x)(1-x)^3). (End)
%e The odd terms of A120070 build the irregular triangle
%e 3;
%e 5;
%e 15,7;
%e 21,9;
%e 35,27,11;
%e 45,33,13;
%e 63,55,39,15;
%e The leftmost column defines this sequence.
%t A142717[n_]:=(n+1)^2-If[OddQ[n],1,4];Array[A142717,100] (* or *)
%t LinearRecurrence[{2,0,-2,1},{3,5,15,21},100] (* _Paolo Xausa_, Dec 05 2023 *)
%Y Cf. A000466, A078371, A100181.
%K nonn
%O 1,1
%A _Paul Curtz_, Sep 26 2008
%E Edited and extended by _R. J. Mathar_, Oct 24 2008
|
