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%I #20 Oct 05 2017 13:26:25
%S 18,126,168,216,468,918,1026,1140,1260,1518,1950,2106,2268,2790,3168,
%T 3996,4218,5418,5676,5940,6210,6768,7056,7650,8268,8910,9240,9576,
%U 9918,10266,10620,11346,11718,13668,14076,15336,15768,16650,17556,18018,18486,18960,20418,21420,22446
%N Numbers equal to the sum of three oblong numbers in arithmetic progression.
%C Subsequence of A028896.
%F a(n) = 3*A292316(n).
%e 126 = 3*4 + 6*7 + 8*9 = 12 + 42 + 72, with 72 - 42 = 42 - 12 = 30;
%e 468 = 8*9 + 12*13 + 15*16 = 72 + 156 + 240, with 240 - 156 = 156 - 72 = 84.
%t o[n_] := n(n+1); s[x_] := Reduce[ x+k == o[y] && x-k == o[z] && k>0 && z>0, {z, y, k}, Integers]; 3 Select[o@ Range@ 93, s[#] =!= False &] (* _Giovanni Resta_, Sep 18 2017 *)
%o (PARI) t=2; k=2; while(t<=10^4, i=k; e=0; v=t+i; while(i>2&&e==0, if(issquare(4*v+1), m=3*t; e=1; print1(m,", ")); i+=-2; v+=i); k+=2; t+=k)
%Y Cf. A292309, A292310, A292313, A292316.
%K nonn
%O 1,1
%A _Antonio Roldán_, Sep 14 2017
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