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 A183575 a(n) = n - 1 + ceiling((n^2-2)/2); complement of A183574. 4
 0, 2, 6, 10, 16, 22, 30, 38, 48, 58, 70, 82, 96, 110, 126, 142, 160, 178, 198, 218, 240, 262, 286, 310, 336, 362, 390, 418, 448, 478, 510, 542, 576, 610, 646, 682, 720, 758, 798, 838, 880, 922, 966, 1010, 1056, 1102, 1150, 1198, 1248, 1298, 1350, 1402, 1456, 1510, 1566, 1622, 1680, 1738, 1798, 1858, 1920, 1982, 2046, 2110, 2176, 2242, 2310, 2378, 2448, 2518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Agrees with the circumference of the n X n stacked book graph for n = 2 up to at least n = 8. - Eric W. Weisstein, Dec 05 2017 It seems that a(n-1) is the maximal length of an optimal solution path required to solve any n X n maze. Here the maze has a single start point, a single end point, and any number of walls that cannot be traversed. The maze is 4-connected, so the allowed moves are: up, down, left and right. For odd n, the hardest mazes have walls located in a spiral, start point in one corner and end point in the center. - Dmitry Kamenetsky, Mar 06 2018 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Graph Circumference. Eric Weisstein's World of Mathematics, Stacked Book Graph. Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = n - 1 + ceiling(n^2/2-1). a(n) = A000217(n-2) + A047215(n-1). - Wesley Ivan Hurt, Jul 15 2013 From Colin Barker, Dec 07 2017: (Start) G.f.: 2*x*(1 + x - x^2) / ((1 - x)^3*(1 + x)). a(n) = (n^2 + 2*n - 4)/2 for n even. a(n) = (n^2 + 2*n - 3)/2 for n odd. a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 4. (End) Sum_{n>=2} 1/a(n) = 7/8 + tan(sqrt(5)*Pi/2)*Pi/(2*sqrt(5)). - Amiram Eldar, Sep 16 2022 MATHEMATICA Table[Ceiling[n^2/2 - 1] + n - 1, {n, 20}] (* Eric W. Weisstein, May 18 2017 *) Table[(2 n (n + 2) - 7 - (-1)^n)/4, {n, 20}] (* Eric W. Weisstein, May 18 2017 *) Table[If[Mod[n, 2] == 0, n^2 + 2 n - 4, (n + 3) (n - 1)]/2, {n, 20}] (* Eric W. Weisstein, May 18 2017 *) LinearRecurrence[{2, 0, -2, 1}, {0, 2, 6, 10}, 80] (* Harvey P. Dale, Feb 19 2021 *) PROG (PARI) concat(0, Vec(2*x*(1 + x - x^2) / ((1 - x)^3*(1 + x)) + O(x^60))) \\ Colin Barker, Dec 07 2017 CROSSREFS Cf. A183574 (complement). Sequence in context: A195957 A354425 A294013 * A096184 A254829 A030511 Adjacent sequences: A183572 A183573 A183574 * A183576 A183577 A183578 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jan 05 2011 EXTENSIONS Description corrected by Eric W. Weisstein, May 18 2017 a(1)=0 inserted by Amiram Eldar, Sep 16 2022 STATUS approved

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Last modified December 6 11:50 EST 2022. Contains 358632 sequences. (Running on oeis4.)