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

1,1

Comments

Subsequence of A028896.

Links

Table of n, a(n) for n=1..45.

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