

A298801


Fourth column of triangular array in A296339.


1



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
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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(n1) + a(n3)  a(n4) for n>11.
(End)


CROSSREFS

Cf. A296339, A004482, A004483, A296340.
Sequence in context: A241284 A019322 A257301 * A016503 A319614 A010653
Adjacent sequences: A298798 A298799 A298800 * A298802 A298803 A298804


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Feb 02 2018


STATUS

approved



