A333836 - 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

A333836

Number of ways to write n as the difference of two positive k-gonal numbers for k >= 3.

0, 1, 2, 2, 4, 2, 5, 3, 6, 3, 6, 4, 7, 4, 7, 5, 8, 4, 7, 5, 10, 6, 7, 5, 10, 5, 10, 5, 9, 7, 9, 6, 11, 6, 10, 6, 12, 5, 11, 7, 11, 6, 9, 7, 13, 9, 9, 8, 12, 7, 13, 7, 9, 7, 11, 9, 17, 7, 7, 8, 13, 6, 14, 9, 17, 8, 11, 6, 12, 9, 11, 9, 13, 7

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

OFFSET

1,3

COMMENTS

Records occur at indices 1, 2, 3, 5, 7, 9, 13, 17, 21, 33, 37, 45, 57, 105, 145, 217, 225, 273, 385, 495, 561, 651, 705, 945, 1105, ... - Peter Kagey, Nov 18 2020

LINKS

Peter Kagey, Table of n, a(n) for n = 1..5000

OEIS Wiki, Figurate numbers: Polygonal numbers

FORMULA

a(n) = A333822(n) - A177025(n) for n > 2.

EXAMPLE

The a(9) = 6 ways of writing 9 as the difference of two k-gonal numbers are:

A000217(4) - A000217(1) = 10 - 1 (triangular),

A000217(5) - A000217(3) = 15 - 6 (triangular),

A000217(9) - A000217(8) = 45 - 36 (triangular),

A000290(5) - A000290(4) = 25 - 16 (square),

A000384(3) - A000384(2) = 15 - 6 (hexagonal), and