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 A042948 Numbers congruent to 0 or 1 mod 4. 64
 0, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Maximum number of squares attacked by a bishop on an (n + 1) X (n + 1) chessboard. - Stewart Gordon, Mar 23 2001 Maximum vertex degree of the (n + 1) X (n + 1) bishop graph and black bishop graph. - Eric W. Weisstein, Jun 26 2017 Also number of squares attacked by a bishop on a toroidal chessboard. - Diego Torres (torresvillarroel(AT)hotmail.com), May 30 2001 Numbers n such that {1, 2, 3, ..., n-1, n} is a perfect Skolem set. - Emeric Deutsch, Nov 24 2006 The number of terms which lie on the principal diagonals of an n X n square spiral. - William A. Tedeschi, Mar 02 2008 Possible nonnegative discriminants of quadratic equation a*x^2 + b*x + c or discriminants of binary quadratic forms a*x^2 + b*x*y + c^y^2. - Artur Jasinski, Apr 28 2008 A133872(a(n)) = 1; complement of A042964. - Reinhard Zumkeller, Oct 03 2008 Partial sums of A035608. - Jaroslav Krizek, Dec 18 2009 Nonnegative m for which floor(k*m/4) = k*floor(m/4), where k = 2 or 3. Example: 13 is in the sequence because floor(2*13/4) = 2*floor(13/4), and also floor(3*13/4) = 3*floor(13/4). - Bruno Berselli, Dec 09 2015 Also number of maximal cliques in the n X n white bishop graph. - Eric W. Weisstein, Dec 01 2017 The offset should have been 1. - Jianing Song, Oct 06 2018 Numbers n for which the binomial coefficient C(n,2) is even. - Tanya Khovanova, Oct 20 2018 LINKS James Spahlinger, Table of n, a(n) for n = 0..10000 H. W. Gould, The inverse of a finite series and a third-order recurrent sequence, Fibonacci Quart. 44 (2006), no. 4, 302-315. See p. 311. T. Skolem, On certain distributions of integers in pairs with given differences, Math. Scand., 1957, vol. 5, 57-68. Harry Tamvakis and O. P. Lossers, Amenable Numbers: 10454, The American Mathematical Monthly, Vol. 105, No. 4 (Apr., 1998), p. 368. Eric Weisstein's World of Mathematics, Bishop Graph Eric Weisstein's World of Mathematics, Black Bishop Graph Eric Weisstein's World of Mathematics, Maximal Clique Eric Weisstein's World of Mathematics, Maximum Vertex Degree Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA a(n) = A042963(n+1) - 1. [Corrected by Jianing Song, Oct 06 2018] G.f.: x*(1 + 3*x)/((1 + x)*(1 - x)^2). a(n) = a(n-1) + 2 + (-1)^n. - Michael Somos, Jan 12 2000 a(n) = -1/2 + 1/2*(-1)^n + 2*n. - Paolo P. Lava, Oct 03 2008 a(n) = 4*n - a(n-1) - 3 with a(0) = 0. - Vincenzo Librandi, Nov 17 2010 a(n) = Sum_{k>=0} A030308(n,k)*A151821(k+1). - Philippe Deléham, Oct 17 2011 a(n) = floor((4/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012 a(n) = n + 2*floor(n/2) = 2*n - (n mod 2). - Bruno Berselli, Apr 30 2016 E.g.f.: 2*exp(x)*x - sinh(x). - Stefano Spezia, Sep 09 2019 MAPLE a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+4 od: seq(a[n], n=0..54); # Zerinvary Lajos, Mar 16 2008 MATHEMATICA Select[Range[0, 150], Or[Mod[#, 4] == 0, Mod[#, 4] == 1] &] (* Vincenzo Librandi, Dec 09 2015 *) Table[((4 n - 5) - (-1)^n)/2, {n, 20}] (* Eric W. Weisstein, Dec 01 2017 *) LinearRecurrence[{1, 1, -1}, {1, 4, 5}, {0, 20}] (* Eric W. Weisstein, Dec 01 2017 *) CoefficientList[Series[x (1 + 3 x)/((-1 + x)^2 (1 + x)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2017 *) PROG (PARI) a(n)=2*n-n%2; (Maxima) makelist(-1/2+1/2*(-1)^n+2*n, n, 0, 60); /* Martin Ettl, Nov 05 2012 */ (MAGMA) [n: n in [0..150]|n mod 4 in {0, 1}]; // Vincenzo Librandi, Dec 09 2015 (PARI) concat(0, Vec(x*(1+3*x)/((1+x)*(1-x)^2) + O(x^100))) \\ Altug Alkan, Dec 09 2015 CROSSREFS Sequence in context: A284906 A285260 A190671 * A126001 A321333 A269984 Adjacent sequences:  A042945 A042946 A042947 * A042949 A042950 A042951 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 20 02:54 EDT 2019. Contains 328244 sequences. (Running on oeis4.)