A244503 Number of ways to place 5 points on an n X n X n triangular grid so that no pair of them has distance sqrt(3).

9, 339, 3606, 24474, 121077, 475353, 1568712, 4524540, 11722134, 27828138, 61442460, 127616970, 251577939, 474068124, 858822579, 1502804622, 2549955858, 4209357693, 6778862319, 10675429650, 16473604089, 24953782251, 37162160802, 54484513344, 78736227726

Offset

4,1

Comments

sqrt(3) is the second closest (Euclidean) distance for a pair of points in a triangular grid. For illustration see A244500.

All elements of the sequence are multiples of 3.

Links

Heinrich Ludwig, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n) = 1/3840*n^10 + 1/768*n^9 - 13/384*n^8 - 7/384*n^7 + 1589/768*n^6 - 24619/3840*n^5 - 1561/32*n^4 + 20965/64*n^3 - 11101/240*n^2 - 85143/20*n + 9711 for n >= 7.

G.f.: -3*x^4*(5*x^13 - 15*x^12 - 26*x^11 + 228*x^10 - 584*x^9 + 706*x^8 - 162*x^7 - 542*x^6 + 766*x^5 - 924*x^4 + 656*x^3 + 124*x^2 + 80*x + 3) / (x - 1)^11. - Colin Barker, Jun 29 2014

Mathematica

CoefficientList[Series[-3*(5*x^13 -15*x^12 -26*x^11 +228*x^10 -584*x^9 +706*x^8 -162*x^7 -542*x^6 +766*x^5 -924*x^4 +656*x^3 +124*x^2 +80*x +3) / (x-1)^11, {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 03 2014 after Colin Barker *)

Crossrefs

Cf. A086274, A244500, A244501, A244502.

Sequence in context: A196883 A012105 A100569 * A152553 A090087 A090085

Adjacent sequences: A244500 A244501 A244502 * A244504 A244505 A244506

Keyword

nonn,easy

Author

Heinrich Ludwig, Jun 29 2014

Status

approved