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 A292314 Numbers equal to the sum of three oblong numbers in arithmetic progression. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A028896. LINKS FORMULA a(n) = 3*A292316(n). EXAMPLE 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. 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 *) PROG (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) CROSSREFS Cf. A292309, A292310, A292313, A292316. Sequence in context: A037064 A077960 A107971 * A002424 A101378 A107417 Adjacent sequences:  A292311 A292312 A292313 * A292315 A292316 A292317 KEYWORD nonn AUTHOR Antonio Roldán, Sep 14 2017 STATUS approved

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