A333868 - OEIS

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A333868

The number of ways to write n as the difference of two k-simplex numbers for k >= 2.

1, 3, 3, 4, 5, 4, 3, 6, 7, 4, 4, 4, 5, 9, 4, 4, 5, 5, 7, 9, 4, 4, 4, 6, 4, 7, 7, 4, 7, 5, 3, 6, 6, 11, 9, 4, 4, 6, 4, 4, 6, 4, 5, 11, 5, 4, 4, 6, 6, 6, 5, 4, 7, 12, 8, 6, 4, 4, 6, 4, 4, 8, 5, 8, 9, 4, 4, 7, 8, 4, 5, 4, 5, 8, 4, 8, 9, 4, 5, 8, 4, 6, 10, 7, 4, 6

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OFFSET

2,2

COMMENTS

a(n) >= A001227(n) + A307666(n).

a(n) >= A003016(n) + A003016(n+1) - 2.

Records occur at indices 2, 3, 5, 6, 9, 10, 15, 35, 55, 105, 210, 1365, 2925, 3003,...

LINKS

Peter Kagey, Table of n, a(n) for n = 2..5000

EXAMPLE

The a(9) = 6 ways to write 9 as the difference of k-simplex numbers for k > 2 are:

C(5, 2) - C(2, 2) = 10 - 1,