A333601 Number of integers from 0 to the triangular number A000217(n) that cannot be represented as a difference of triangular numbers from 0 to n.

0, 0, 0, 1, 1, 3, 5, 7, 9, 12, 15, 19, 23, 28, 35, 43, 47, 52, 61, 67, 76, 85, 94, 105, 114, 125, 137, 149, 161, 175, 190, 203, 216, 232, 246, 261, 278, 292, 309, 329, 346, 365, 384, 404, 426, 449, 470, 493, 516, 536, 562, 587, 611, 637, 665, 691, 719, 746, 770, 800, 831, 860, 889, 923, 951, 983

Offset

0,6

Links

Table of n, a(n) for n=0..65.

Formula

a(n) = A000217(n) - A334821(n) + 1.

Example

a(2) = 0 as all four numbers from 0 to A000217(2) = 3 can be represented as a difference of 0,1,3, the triangular numbers from 0 to 2.
a(3) = 1 as in the seven numbers from 0 to A000217(3) = 6, one number, 4, cannot be represented as a difference of 0,1,3,6, the triangular numbers from 0 to 3. The other five numbers can be.
a(6) = 5 as in the twenty-two numbers from 0 to A000217(6) = 21, five numbers, 8,13,16,17,19, cannot be represented as a difference of 0,1,3,6,10,15,21, the triangular numbers from 0 to 6. The other seventeen numbers can be.

Crossrefs

Cf. A334821, A234813, A000217, A001227.

Sequence in context: A007078 A226332 A226331 * A316312 A362128 A118015

Adjacent sequences: A333598 A333599 A333600 * A333602 A333603 A333604

Keyword

nonn

Author

Scott R. Shannon, Jun 09 2020

Status

approved