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A333836 Number of ways to write n as the difference of two positive k-gonal numbers for k >= 3. 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

A001107(2) - A001107(1) = 10 -  1 (10-gonal).

MATHEMATICA

b := 74

CoefficientList[

Series[Sum[

   Sum[x^(k*(p*k - (p - 2))/2)*x^(p*k)/(1 - x^(p*k)), {k, 1, b}], {p,

    1, b - 1}], {x, 0, b}], x]

CROSSREFS

Cf. A177025, A333822.

Cf. A000217, A000290, A000384, A001107.

Sequence in context: A129296 A300837 A321443 * A125296 A294097 A233520

Adjacent sequences:  A333833 A333834 A333835 * A333837 A333838 A333839

KEYWORD

nonn

AUTHOR

Peter Kagey, Apr 07 2020

STATUS

approved

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Last modified June 20 00:16 EDT 2021. Contains 345154 sequences. (Running on oeis4.)