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A297740 The number of distinct positions on an infinite chess board reachable by the (2,3)-leaper in <= n moves. 4
1, 9, 41, 129, 321, 625, 997, 1413, 1885, 2425, 3033, 3709, 4453, 5265, 6145, 7093, 8109, 9193, 10345, 11565, 12853, 14209, 15633, 17125, 18685, 20313, 22009, 23773, 25605, 27505, 29473, 31509, 33613, 35785, 38025, 40333, 42709, 45153, 47665, 50245, 52893 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

R. J. Mathar, Fairy chess leaper minimum moves on the infinite chessboard (2018)

FORMULA

a(n) = 34*n^2+30*n+9 for n>=6.

From Colin Barker, Jan 05 2018: (Start)

G.f.: (1 + x)*(1 + 5*x + 12*x^2 + 20*x^3 + 28*x^4 - 20*x^5 - 24*x^6 + 12*x^8) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

PROG

(PARI) Vec((1 + x)*(1 + 5*x + 12*x^2 + 20*x^3 + 28*x^4 - 20*x^5 - 24*x^6 + 12*x^8) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Jan 07 2018

CROSSREFS

Cf. A018836 (1,2)-leaper or (1,3)-leaper, A297741 (3,4)-leaper.

Partial sums of A018839.

Cf. A253974, A254129, A254459.

Sequence in context: A018836 A245932 A274323 * A297741 A001846 A271663

Adjacent sequences:  A297737 A297738 A297739 * A297741 A297742 A297743

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Jan 05 2018

STATUS

approved

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Last modified May 22 00:03 EDT 2018. Contains 304403 sequences. (Running on oeis4.)