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 A302298 Wiener index of the graph of nodes (i,j) of the square lattice such that abs(i) + abs(j) <= n. 0
 0, 16, 192, 1008, 3504, 9504, 21840, 44576, 83232, 145008, 239008, 376464, 570960, 838656, 1198512, 1672512, 2285888, 3067344, 4049280, 5268016, 6764016, 8582112, 10771728, 13387104, 16487520, 20137520, 24407136, 29372112, 35114128, 41721024, 49287024, 57912960, 67706496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The considered grid distance is the Manhattan distance (taxicab metric). LINKS Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Wiener Index Eric Weisstein's World of Mathematics, Taxicab Metric FORMULA Conjectures from Colin Barker, Apr 08 2018: (Start) G.f.: 16*x*(1 + x)*(1 + 5*x + x^2) / (1 - x)^6. a(n) = 2*(n*(6 + 25*n + 40*n^2 + 35*n^3 + 14*n^4)) / 15. a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5. (End) MATHEMATICA a[n_]:=(1/2)*Sum[Sum[Sum[Sum[ Abs[i2-i1] + Abs[j2-j1], {j1, Abs[i1]-n, n-Abs[i1]}], {i1, -n, n}], {j2, Abs[i2]-n, n-Abs[i2]}], {i2, -n, n}]; Table[a[n], {n, 0, 32}] CROSSREFS Cf. A292053, A143945. Sequence in context: A321456 A304307 A316206 * A305773 A317122 A230832 Adjacent sequences:  A302295 A302296 A302297 * A302299 A302300 A302301 KEYWORD nonn AUTHOR Andres Cicuttin, Apr 04 2018 STATUS approved

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Last modified June 22 10:52 EDT 2021. Contains 345375 sequences. (Running on oeis4.)