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 A213041 Number of (w,x,y) with all terms in {0..n} and 2|w-x| = max(w,x,y)-min(w,x,y). 2
 1, 2, 7, 12, 21, 30, 43, 56, 73, 90, 111, 132, 157, 182, 211, 240, 273, 306, 343, 380, 421, 462, 507, 552, 601, 650, 703, 756, 813, 870, 931, 992, 1057, 1122, 1191, 1260, 1333, 1406, 1483, 1560, 1641, 1722, 1807, 1892, 1981, 2070, 2163, 2256 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A212959 for a guide to related sequences. For n > 3, a(n-2) is the number of distinct values of the magic constant in a perimeter-magic (n-1)-gon of order n (see A342819). - Stefano Spezia, Mar 23 2021 LINKS Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 10-13). Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3. G.f.: (1 + 3*x^2)/((1 - x)^3 * (1 + x)). a(n) = (n+1)^2 - 2*A004526(n-1) - 2. - Wesley Ivan Hurt, Jul 15 2013 a(n) = A002620(n+2) + 3*A002620(n). - R. J. Mathar, Jul 15 2013 a(n)+a(n+1) = A058331(n+1). - R. J. Mathar, Jul 15 2013 a(n) = n*(n+1)+(1+(-1)^n)/2. - Wesley Ivan Hurt, May 06 2016 E.g.f.: x*(x + 2)*exp(x) + cosh(x). - Ilya Gutkovskiy, May 06 2016 MATHEMATICA t = Compile[{{n, _Integer}}, Module[{s = 0}, (Do[If[Max[w, x, y] - Min[w, x, y] == 2 Abs[w - x], s = s + 1], {w, 0, n}, {x, 0, n}, {y, 0, n}]; s)]]; m = Map[t[#] &, Range[0, 45]]   (* A213041 *) PROG (PARI) Vec((1+3*x^2)/((1-x)^3*(1+x)) + O(x^99)) \\ Altug Alkan, May 06 2016 CROSSREFS Cf. A002620, A004526, A058331, A212959, A168277 (first differences), A342819. Sequence in context: A309150 A333354 A119713 * A293330 A135541 A288656 Adjacent sequences:  A213038 A213039 A213040 * A213042 A213043 A213044 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 10 2012 STATUS approved

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Last modified June 25 08:27 EDT 2021. Contains 345453 sequences. (Running on oeis4.)