A297741 The number of distinct positions on an infinite chessboard reachable by the (3,4)-leaper in <= n moves.

1, 9, 41, 129, 321, 681, 1289, 2121, 3081, 4121, 5233, 6445, 7777, 9233, 10813, 12517, 14345, 16297, 18373, 20573, 22897, 25345, 27917, 30613, 33433, 36377, 39445, 42637, 45953, 49393, 52957, 56645, 60457, 64393, 68453, 72637, 76945, 81377, 85933, 90613, 95417

Offset: 0

Author

R. J. Mathar, Jan 05 2018

Keywords

• nonn

Crossrefs

Cf. A018836 (1,2)-leaper or (1,3)-leaper, A297740 (2,3)-leaper.

Formula

Conjecture: a(n) = 62*n^2 + 30*n - 55 for n >= 10.

Conjectures from Colin Barker, Jan 06 2018: (Start)

G.f.: (1 + 6*x + 17*x^2 + 32*x^3 + 48*x^4 + 64*x^5 + 80*x^6 - 24*x^7 - 96*x^8 - 48*x^9 - 8*x^10 + 28*x^11 + 20*x^12 + 4*x^13) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>13.

(End)