A242067 Number of triangular numbers between n^2 and n^3 (excluding the bounds).

0, 0, 1, 3, 5, 9, 12, 16, 21, 25, 31, 36, 42, 48, 54, 61, 68, 75, 83, 90, 98, 106, 115, 123, 132, 142, 150, 160, 170, 180, 190, 200, 211, 221, 232, 243, 254, 266, 277, 289, 301, 313, 326, 338, 351, 363, 376, 390, 402, 416, 429, 443, 456, 471, 485, 499, 514, 528, 543, 558

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

There are 3 triangular numbers between 9 and 27, namely 10, 15, 21. So a(3)=3.

Maple

b:= n-> floor((sqrt(n*8+1)-1)/2):
a:= n-> `if`(n<2, 0, b(n^3-1) -b(n^2)):
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 14 2014

Prog

(Python)
for n in range(60):
  sq=n*n
  cb=n**3
  s = t = 0
  while 1:
    tn = t*(t+1)/2
    if tn>sq and tn<cb:  s+=1
    elif tn>=cb:  break
    t+=1
  print str(s)+', ',
(PARI) a(n) = sum(i=n^2+1, n^3-1, ispolygonal(i, 3)); \\ Michel Marcus, Aug 14 2014

Crossrefs

Cf. A000217, A000290, A000578.

Sequence in context: A259368 A175098 A351389 * A127722 A234813 A060419

Adjacent sequences: A242064 A242065 A242066 * A242068 A242069 A242070

Keyword

nonn,easy

Author

Alex Ratushnyak, Aug 13 2014

Status

approved