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 A286429 Highest elevation of an island above sea level in a number square. 1
 0, 0, 0, 0, 16, 27, 40, 55, 72, 91, 112, 135, 160, 187, 216, 247, 280, 315, 352, 391, 432, 475, 520, 567, 616, 667, 720, 775, 832, 891, 952, 1015, 1080, 1147, 1216, 1287, 1360, 1435, 1512, 1591, 1672, 1755, 1840, 1927, 2016, 2107, 2200, 2295, 2392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The water retention model for mathematical surfaces has previously looked at lakes and ponds. This sequence looks at the maximum possible height of an island above water level in a number square. The smallest possible water elevation will always be composed of an eight-cell lake or pond with a spillway value of nine. This moat is not centered in a(n) > 5 but has the square's edge as one of its borders. A number square contains the numbers 1 to n^2 without repeats. The larger terms in this sequence are a(n) = n*(n+6) or A028560. LINKS Wikipedia, Water retention on mathematical surfaces FORMULA Conjectures from Colin Barker, May 09 2017: (Start) G.f.: x^4*(16 - 21*x + 7*x^2) / (1 - x)^3. a(n) = n^2 + 2*n - 8 for n>3. a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6. (End) EXAMPLE For the 6 X 6 number square the largest value is 36 which is assigned to the single-cell island. I only include the pertinent moat, spillway, and island values for the 6 X 6 example. ( 1   2   3    ) ( 8  36   4  9 ) ( 7   6   5    ) CROSSREFS Cf. A054247, A201126. Sequence in context: A118642 A088247 A032610 * A329206 A280935 A067650 Adjacent sequences:  A286426 A286427 A286428 * A286430 A286431 A286432 KEYWORD nonn AUTHOR Craig Knecht, May 09 2017 STATUS approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)