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 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). 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 3 23:57 EDT 2023. Contains 363118 sequences. (Running on oeis4.)