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A327692 Number of length-n phone numbers that can be dialed by a chess knight on a 0-9 keypad that starts on any number and takes n-1 steps. 1
10, 20, 46, 104, 240, 544, 1256, 2848, 6576, 14912, 34432, 78080, 180288, 408832, 944000, 2140672, 4942848, 11208704, 25881088, 58689536, 135515136, 307302400, 709566464, 1609056256, 3715338240, 8425127936, 19453763584 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The keypad is of the form:

+---+---+---+

| 1 | 2 | 3 |

+---+---+---+

| 4 | 5 | 6 |

+---+---+---+

| 7 | 8 | 9 |

+---+---+---+

| * | 0 | # |

+---+---+---+

LINKS

Derek Lim, Table of n, a(n) for n = 1..2500

FORMULA

Conjectures from Colin Barker, Oct 01 2019: (Start)

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

a(n) = 6*a(n-2) - 4*a(n-4) for n>6.

(End)

EXAMPLE

For n = 1 the a(1) = 10 numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

For n = 2 the a(2) = 20 numbers are 04, 06, 16, 18, 27, 29, 34, 38, 43, 49, 40, 61, 67, 60, 72, 76, 81, 83, 92, 94.

PROG

(Python)

def number_dialable(N):

    reach = ((4, 6), (6, 8), (7, 9), (4, 8), (3, 9, 0), (), (1, 7, 0), (2, 6), (1, 3), (2, 4))

    M = [[0] * 10 for _ in range(N)]

    M[0] = [1]*10

    for step in range(1, N):

        for tile in range(10):

            for nxt in reach[tile]:

                M[step][nxt] += M[step-1][tile]

    return [sum(row) for row in M]

CROSSREFS

Cf. A280594, A169696.

Sequence in context: A048063 A007927 A284991 * A269234 A160517 A072081

Adjacent sequences:  A327689 A327690 A327691 * A327693 A327694 A327695

KEYWORD

nonn

AUTHOR

Derek Lim, Sep 22 2019

STATUS

approved

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Last modified November 15 11:18 EST 2019. Contains 329144 sequences. (Running on oeis4.)