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Triangle read by rows, n-th row = n terms of 2n, 2n+2, 2n+4, ..., 1; with a(1) = 1.
3

%I #11 Feb 08 2022 20:19:03

%S 1,4,1,6,8,1,8,10,12,1,10,12,14,16,1,12,14,16,18,20,1,14,16,18,20,22,

%T 24,1,16,18,20,22,24,26,28,1,18,20,22,24,26,28,30,32,1,20,22,24,26,28,

%U 30,32,34,36,1

%N Triangle read by rows, n-th row = n terms of 2n, 2n+2, 2n+4, ..., 1; with a(1) = 1.

%C Row sums = A056108: (1, 5, 15, 31, 53, ...).

%H Robert Israel, <a href="/A134234/b134234.txt">Table of n, a(n) for n = 1..10011</a>

%F G.f.: 2*x/(1-x)^2 - 2*(2-x)/(1-x)*Sum_{n>=1} n*x^(n*(n+1)/2) + (3-x)/(1-x)*Sum_{n>=1} x^(n*(n+1)/2). - _Robert Israel_, Jan 15 2016

%e First few rows of the triangle:

%e 1;

%e 4, 1;

%e 6, 8, 1;

%e 8, 10, 12, 1;

%e 10, 12, 14, 16, 1;

%e ...

%p seq(op([seq(2*n+2*k,k=0..n-2),1]),n=1..10); # _Robert Israel_, Jan 15 2016

%t Flatten[Table[Join[{1},Range[n,2n-3,2]],{n,4,30,2}]] (* _Harvey P. Dale_, Nov 06 2013 *)

%Y Cf. A056108.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Oct 14 2007