

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
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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] && xk == 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



