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 A098499 Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the diagonal. 4
 1, 5, 23, 57, 109, 169, 246, 334, 439, 555, 688, 832, 993, 1165, 1354, 1554, 1771, 1999, 2244, 2500, 2773, 3057, 3358, 3670, 3999, 4339, 4696, 5064, 5449, 5845, 6258, 6682, 7123, 7575, 8044, 8524, 9021, 9529, 10054, 10590, 11143, 11707, 12288, 12880, 13489 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = (1/4) [28n^2 - 6n + 9 + 3(-1)^n], for n>3. G.f.: -(3*x^7-x^6-8*x^5+4*x^4+13*x^3+13*x^2+3*x+1) / ((x-1)^3*(x+1)). - Colin Barker, Jul 14 2013 EXAMPLE 5 squares are reachable after 1 move, from these you can reach 18 new squares more, so a(1)=5, a(2)=23. CROSSREFS Equals A098498(n) - A052938(n-4), n>3. See A018836 (unbounded), A098498 (halfplane), A098500 (quadrant), A098501 (octant). Sequence in context: A186030 A092544 A319087 * A075565 A075707 A126420 Adjacent sequences:  A098496 A098497 A098498 * A098500 A098501 A098502 KEYWORD nonn,easy AUTHOR Ralf Stephan, Sep 15 2004 EXTENSIONS More terms from Colin Barker, Jul 14 2013 STATUS approved

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Last modified May 16 12:30 EDT 2021. Contains 343947 sequences. (Running on oeis4.)