

A128549


Difference between triangular number and next perfect square.


2



3, 1, 3, 6, 1, 4, 8, 13, 4, 9, 15, 3, 9, 16, 1, 8, 16, 25, 6, 15, 25, 3, 13, 24, 36, 10, 22, 35, 6, 19, 33, 1, 15, 30, 46, 10, 26, 43, 4, 21, 39, 58, 15, 34, 54, 8, 28, 49, 71, 21, 43, 66, 13, 36, 60, 4, 28, 53, 79, 19, 45, 72, 9, 36, 64, 93, 26, 55, 85, 15, 45, 76, 3, 34, 66, 99, 22
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OFFSET

1,1


COMMENTS

If a(n)=1 then such n gives the sequence A006451 (triangular numbers whose distance to the nearest bigger perfect square is 1). [From Ctibor O. Zizka, Oct 07 2009]


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = (floor(sqrt(n(n+1)/2))+1)^2n(n+1)/2.


EXAMPLE

a(1)=2^21(1+1)/2=3, a(2)=2^22(2+1)/2=1, a(3)=3^23(3+1)/2=3, a(3)=4^24(4+1)/2=6.


MAPLE

f:= n > (floor(sqrt(n*(n+1)/2))+1)^2n*(n+1)/2:
map(f, [$1..100]); # Robert Israel, Jan 21 2020


MATHEMATICA

Table[(Floor[Sqrt[n(n+1)/2]]+1)^2n(n+1)/2, {n, 100}]
(Floor[Sqrt[#]]+1)^2#&/@Accumulate[Range[100]] (* Harvey P. Dale, Oct 15 2014 *)


CROSSREFS

Cf. A000217, A000290, A006451.
Sequence in context: A181843 A131111 A336574 * A055885 A181425 A174505
Adjacent sequences: A128546 A128547 A128548 * A128550 A128551 A128552


KEYWORD

nonn


AUTHOR

Zak Seidov, May 08 2007


STATUS

approved



