A292314 Numbers equal to the sum of three oblong numbers in arithmetic progression.

18, 126, 168, 216, 468, 918, 1026, 1140, 1260, 1518, 1950, 2106, 2268, 2790, 3168, 3996, 4218, 5418, 5676, 5940, 6210, 6768, 7056, 7650, 8268, 8910, 9240, 9576, 9918, 10266, 10620, 11346, 11718, 13668, 14076, 15336, 15768, 16650, 17556, 18018, 18486, 18960, 20418, 21420, 22446

Offset: 1

Author

Antonio Roldán, Sep 14 2017

Keywords

• nonn

Comments

Subsequence of A028896.

Examples

			126 = 3*4 + 6*7 + 8*9 = 12 + 42 + 72, with 72 - 42 = 42 - 12 = 30;
468 = 8*9 + 12*13 + 15*16 = 72 + 156 + 240, with 240 - 156 = 156 - 72 = 84.
		

Crossrefs

Cf. A292309, A292310, A292313, A292316.

Programs

Mathematica

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 *)

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)

Formula

a(n) = 3*A292316(n).