A333601 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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