

A287733


First differences of A069497.


1



6, 30, 30, 12, 42, 90, 66, 24, 78, 150, 102, 36, 114, 210, 138, 48, 150, 270, 174, 60, 186, 330, 210, 72, 222, 390, 246, 84, 258, 450, 282, 96, 294, 510, 318, 108, 330, 570, 354, 120, 366, 630, 390, 132, 402, 690, 426, 144, 438, 750, 462, 156, 474, 810, 498, 168, 510, 870, 534
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OFFSET

1,1


COMMENTS

First differences of the subsequence of triangular numbers that are divisible by 6.
By definition, these numbers are themselves divisible by 6.


LINKS

Table of n, a(n) for n=1..59.


FORMULA

G.f.: 6*(x^2+4*x+1)*(x^2x+1)/((x1)^2*(x^2+1)^2).  Robert Israel, May 30 2017


EXAMPLE

The first triangular number divisible by 6 is 6, and the second triangular number divisible by 6 is 36. Therefore a(2) = 36  6 = 30. (The zeroeth triangular number divisible by 6 is taken to be 0.)


MAPLE

S:= [seq(seq((12*i+j)*(12*i+j+1)/2, j=[0, 3, 8, 11]), i=0..50)]:
S[2..1]S[1..2]; # Robert Israel, May 30 2017


MATHEMATICA

Differences@ Select[Array[# (# + 1)/2 &, 180, 0], Mod[#, 6] == 0 &] (* Robert G. Wilson v, May 30 2017 *)
Differences[Select[Accumulate[Range[0, 209]], Divisible[#, 6] &]] (* Alonso del Arte, May 31 2017 *)


CROSSREFS

Cf. A069497, A108782, A154293.
Sequence in context: A309253 A260017 A123624 * A066197 A078638 A068510
Adjacent sequences: A287730 A287731 A287732 * A287734 A287735 A287736


KEYWORD

nonn,look


AUTHOR

Greg Huber, May 30 2017


EXTENSIONS

More terms from Robert G. Wilson v, May 30 2017


STATUS

approved



