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 A248825 n^2 + 1 - (-1)^n. 1
 0, 3, 4, 11, 16, 27, 36, 51, 64, 83, 100, 123, 144, 171, 196, 227, 256, 291, 324, 363, 400, 443, 484, 531, 576, 627, 676, 731, 784, 843, 900, 963, 1024, 1091, 1156, 1227, 1296, 1371, 1444, 1523, 1600, 1683, 1764, 1851, 1936, 2027, 2116 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also, A016742 and A164897 interleaved. See the spiral in Example field of A054552: after 0, the sequence is given by the terms of the semidiagonals 4, 16, 36, 64, 100, ... and 3, 11, 27, 51, 83, ... sorted into ascending order. Primes of the sequence are in A056899. LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = a(-n) = 2*a(n-1) - 2*(n-3) + a(n-4). a(n) = n^2 + A010673(n) = (n+1)^2 - A168277(n+1). a(n+1) = A248800(n) + A042963(n+1) = a(n) + A166519(n). a(n+2) = a(n) + 4*n. a(n+5) = a(n-5) + A008602(n). G.f.: x*(3 - 2*x + 3*x^2)/((1 + x)*(1 - x)^3). [Bruno Berselli, Oct 15 2014] MATHEMATICA Table[n^2 + 1 - (-1)^n, {n, 0, 60}] (* Vincenzo Librandi, Oct 16 2014 *) PROG (PARI) vector(100, n, (n-1)^2+1+(-1)^n) \\ Derek Orr, Oct 15 2014 (MAGMA) [n^2+1-(-1)^n: n in [0..60]]; // Vincenzo Librandi, Oct 16 2014 (Sage) [n^2+1-(-1)^n for n in (0..60)] # Bruno Berselli, Oct 16 2014 CROSSREFS Cf. A000290, A008586, A008602, A010673, A016742, A042963, A056899, A164897, A166519, A168277, A248800. Sequence in context: A041527 A290493 A266384 * A001641 A007382 A127804 Adjacent sequences:  A248822 A248823 A248824 * A248826 A248827 A248828 KEYWORD nonn,easy AUTHOR Paul Curtz, Oct 15 2014 EXTENSIONS Edited by Bruno Berselli, Oct 16 2014 STATUS approved

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)