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

0,1

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).

Links

Table of n, a(n) for n=0..78.

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)

Crossrefs

Cf. A296339, A004482, A004483, A296340.

Sequence in context: A241284 A019322 A257301 * A340297 A369928 A016503

Adjacent sequences: A298798 A298799 A298800 * A298802 A298803 A298804

Keyword

nonn

Author

N. J. A. Sloane, Feb 02 2018

Status

approved