

A372718


Triangular numbers that are 2 mod 4, halved.


0



3, 5, 33, 39, 95, 105, 189, 203, 315, 333, 473, 495, 663, 689, 885, 915, 1139, 1173, 1425, 1463, 1743, 1785, 2093, 2139, 2475, 2525, 2889, 2943, 3335, 3393, 3813, 3875, 4323, 4389, 4865, 4935, 5439, 5513, 6045, 6123, 6683, 6765, 7353, 7439, 8055, 8145, 8789, 8883, 9555, 9653
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OFFSET

1,1


COMMENTS

The sum of the first 2*a(n) numbers of any Fibonaccilike sequence equals its (a(n)+2)nd term times the a(n)th Lucas number.


LINKS



FORMULA



EXAMPLE

10 is a triangular number that has a remainder of 2 when divided by 4. Therefore, its half, 5, is in this sequence. Moreover, the sum of the first 5*2 Fibonacci numbers is 143 (not counting zero). This sum is a product of 13, which is the (5+2 = 7)th term of the Fibonacci sequence times 11, which is the fifth Lucas number.


MATHEMATICA

Select[Table[n (n + 1)/2, {n, 200}], Mod[#, 4] == 2 &]/2


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



