A316671 Squares visited by moving diagonally one square on a diagonally numbered board and moving to the lowest available unvisited square at each step.

1, 5, 4, 12, 11, 23, 22, 38, 37, 57, 56, 80, 79, 107, 106, 138, 137, 173, 172, 212, 211, 255, 254, 302, 301, 353, 352, 408, 407, 467, 466, 530, 529, 597, 596, 668, 667, 743, 742, 822, 821, 905, 904, 992, 991, 1083, 1082, 1178, 1177, 1277, 1276, 1380, 1379

Offset

1,2

Comments

Board is numbered as follows:

1 2 4 7 11 16 .

3 5 8 12 17 .

6 9 13 18 .

10 14 19 .

15 20 .

21 .

.

Links

Daniël Karssen, Table of n, a(n) for n = 1..10000

Daniël Karssen, Figure showing the first 6 steps of the sequence

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

From Colin Barker, Jul 18 2018: (Start)

G.f.: x*(1 + 4*x - 3*x^2 + 2*x^4) / ((1 - x)^3*(1 + x)^2).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.

a(n) = (n^2 + n + 4)/2 for n even.

a(n) = (n^2 - n + 2)/2 for n odd.

(End)

Mathematica

CoefficientList[ Series[-(2x^4 - 3x^2 + 4x + 1)/((x - 1)^3 (x + 1)^2), {x, 0, 52}], x] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 5, 4, 12, 11}, 53] (* Robert G. Wilson v, Jul 18 2018 *)

Prog

(PARI) Vec(x*(1 + 4*x - 3*x^2 + 2*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^40)) \\ Colin Barker, Jul 18 2018

Crossrefs

Cf. A316588, A316668, A316669, A316670.

Sequence in context: A131875 A095871 A284551 * A338157 A189235 A019068

Adjacent sequences: A316668 A316669 A316670 * A316672 A316673 A316674

Keyword

nonn,easy

Author

Daniël Karssen, Jul 15 2018

Status

approved