A334821 Number of integers from 0 to the triangular number A000217(n) that can be represented as a difference of triangular numbers from 0 to n.

1, 2, 4, 6, 10, 13, 17, 22, 28, 34, 41, 48, 56, 64, 71, 78, 90, 102, 111, 124, 135, 147, 160, 172, 187, 201, 215, 230, 246, 261, 276, 294, 313, 330, 350, 370, 389, 412, 433, 452, 475, 497, 520, 543, 565, 587, 612, 636, 661, 690, 714, 740, 768, 795, 821, 850, 878, 908, 942, 971, 1000, 1032, 1065

Offset

0,2

Links

Table of n, a(n) for n=0..62.

Formula

a(n) = A000217(n) - A333601(n) + 1.

Example

a(2) = 4 as all four numbers from 0 to A000217(2) = 3 can all be represented as a difference of 0,1,3, the triangular numbers from 0 to 2.
a(3) = 6 as in the seven numbers from 0 to A000217(3) = 6, six can be represented as a difference of 0,1,3,6, the triangular numbers from 0 to 3. One number, 4, cannot be.
a(6) = 17 as in the twenty-two numbers from 0 to A000217(6) = 21, seventeen can be represented as a difference of 0,1,3,6,10,15,21, the triangular numbers from 0 to 6. Five numbers, 8,13,16,17,19, cannot be.

Crossrefs

Cf. A333601, A234813, A000217, A001227.

Sequence in context: A233556 A087148 A297531 * A275489 A153817 A354673

Adjacent sequences: A334818 A334819 A334820 * A334822 A334823 A334824

Keyword

nonn

Author

Scott R. Shannon, Jun 09 2020

Status

approved