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 A174239 a(n) = (3*n + 1 + (-1)^n*(n+3))/4. 4
 1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, 19, 9, 21, 10, 23, 11, 25, 12, 27, 13, 29, 14, 31, 15, 33, 16, 35, 17, 37, 18, 39, 19, 41, 20, 43, 21, 45, 22, 47, 23, 49, 24, 51, 25, 53, 26, 55, 27, 57, 28, 59, 29, 61, 30, 63, 31, 65, 32, 67, 33, 69, 34, 71, 35, 73, 36, 75, 37, 77, 38, 79, 39, 81 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Obtained from A026741 by swapping pairs of consecutive entries. The main diagonal of an array with this sequence in the top row and further rows defined by the first differences of their previous row is essentially 1 followed by 3*A045623(.): 1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, ... -1, 3, -2, 4, -3, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, ... 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, ... -9, 11, -13, 15, -17, 19, -21, 23, -25, 27, -29, 31, ... 20, -24, 28, -32, 36, -40, 44, -48, 52, -56, 60, -64, ... -44, 52, -60, 68, -76, 84, -92, 100, -108, 116, -124, 132, ... 96, -112, 128, -144, 160, -176, 192, -208, 224, -240, ... Also, numerator of (Nimsum n+1)/2 = A004442(n)/2. - Wesley Ivan Hurt, Mar 21 2015 LINKS Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(2n) = 2n+1; a(2n+1) = n. a(n) = 2*a(n-2) - a(n-4). a(2n+1) - 2*a(2n) = -A016789(n+1). a(2n+2) - 2*a(2n+1) = 3. G.f.: ( 1+x^2+x^3 ) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Feb 07 2011 MAPLE A174239:=n->(3*n+1+(-1)^n*(n+3))/4: seq(A174239(n), n=0..100); # Wesley Ivan Hurt, Mar 21 2015 MATHEMATICA Table[(3 n + 1 + (-1)^n*(n + 3))/4, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 21 2015 *) LinearRecurrence[{0, 2, 0, -1}, {1, 0, 3, 1}, 90] (* Harvey P. Dale, Jul 16 2018 *) PROG (MAGMA) [(3*n+1 +(-1)^n*(n+3))/4: n in [0..80]]; // Vincenzo Librandi, Feb 08 2011 CROSSREFS Cf. A004442. Sequence in context: A225080 A276505 A201901 * A066249 A065168 A318581 Adjacent sequences:  A174236 A174237 A174238 * A174240 A174241 A174242 KEYWORD nonn,easy AUTHOR Paul Curtz, Mar 13 2010 STATUS approved

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Last modified June 15 20:50 EDT 2019. Contains 324145 sequences. (Running on oeis4.)