A298801 Fourth column of triangular array in A296339.

4, 3, 6, 0, 1, 2, 5, 9, 12, 7, 8, 15, 10, 11, 18, 13, 14, 21, 16, 17, 24, 19, 20, 27, 22, 23, 30, 25, 26, 33, 28, 29, 36, 31, 32, 39, 34, 35, 42, 37, 38, 45, 40, 41, 48, 43, 44, 51, 46, 47, 54, 49, 50, 57, 52, 53, 60, 55, 56, 63, 58, 59, 66, 61, 62, 69, 64, 65, 72, 67, 68, 75, 70, 71, 78, 73, 74, 81, 76

Offset: 0

Author

N. J. A. Sloane, Feb 02 2018

Keywords

• nonn

Comments

This was the first column of A296339 for which no simple formula was known (cf. A004483, A004482). (Since these are Grundy values for a certain game, there is a complicated recurrence involving the whole triangle.) The formula below matches the data, and is fairly short (but ugly).

Crossrefs

Cf. A296339, A004482, A004483, A296340.

Formula

It appears that for n >= 8, a(n) = tersum(n,1) + 6 if n == 2 (mod 3), otherwise tersum(n,1) - 3.

Conjectures from Colin Barker, Feb 03 2018: (Start)

G.f.: (4 - x + 3*x^2 - 10*x^3 + 2*x^4 - 2*x^5 + 9*x^6 + 3*x^7 + 2*x^8 - 8*x^9 - 3*x^10 + 4*x^11) / ((1 - x)^2*(1 + x + x^2)).

a(n) = a(n-1) + a(n-3) - a(n-4) for n>11.

(End)