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 A292576 Permutation of the natural numbers partitioned into quadruples [4k-1, 4k-3, 4k-2, 4k], k > 0. 3
 3, 1, 2, 4, 7, 5, 6, 8, 11, 9, 10, 12, 15, 13, 14, 16, 19, 17, 18, 20, 23, 21, 22, 24, 27, 25, 26, 28, 31, 29, 30, 32, 35, 33, 34, 36, 39, 37, 38, 40, 43, 41, 42, 44, 47, 45, 46, 48, 51, 49, 50, 52, 55, 53, 54, 56, 59, 57, 58, 60, 63, 61, 62 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Partition the natural number sequence into quadruples starting with (1,2,3,4); swap the second and third elements, then swap the first and the second element; repeat for all quadruples. LINKS Guenther Schrack, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). Index entries for sequences that are permutations of the natural numbers FORMULA a(1)=3, a(2)=1, a(3)=2, a(4)=4, a(n) = a(n-4) + 4 for n > 4. O.g.f.: (2*x^3 + x^2 - 2*x + 3)/(x^5 - x^4 - x + 1). a(n) = n + ((-1)^(n*(n-1)/2)*(2-(-1)^n) - (-1)^n)/2. a(n) = n + (cos(n*Pi/2) - cos(n*Pi) + 3*sin(n*Pi/2))/2. a(n) = n + n mod 2 + (ceiling(n/2)) mod 2 - 2*(floor(n/2) mod 2). Linear recurrence: a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. First Differences, periodic: (-2, 1, 2, 3), repeat; also (-1)^A130569(n)*A068073(n+2) for n > 0. PROG (MATLAB) a = [3 1 2 4]; % Generate b-file max = 10000; for n := 5:max a(n) = a(n-4) + 4; end; (PARI) for(n=1, 10000, print1(n + ((-1)^(n*(n-1)/2)*(2 - (-1)^n) - (-1)^n)/2, ", ")) CROSSREFS Inverse: A056699(n+1) - 1 for n > 0. Sequence of fixed points: A008586(n) for n > 0. Subsequences: elements with odd index: A042964(A103889(n)) for n > 0. elements with even index: A042948(n) for n > 0. odd elements: A166519(n) for n>0. indices of odd elements: A042963(n) for n > 0. even elements: A005843(n) for n>0. indices of even elements: A014601(n) for n > 0. Sum of pairs of elements: a(n+2) + a(n) = A163980(n+1) = A168277(n+2) for n > 0. Difference between pairs of elements: a(n+2) - a(n) = (-1)^A011765(n+3)*A091084(n+1) for n > 0. Compound relations: a(n) = A284307(n+1) - 1 for n > 0. a(n+2) - 2*a(n+1) + a(n) = (-1)^A011765(n)*A132400(n+1) for n > 0. Compositions: a(n) = A116966(A080412(n)) for n > 0. a(A284307(n)) = A256008(n) for n > 0. a(A042963(n)) = A166519(n-1) for n > 0. A256008(a(n)) = A056699(n) for n > 0. Sequence in context: A120577 A104695 A233904 * A083275 A230892 A325671 Adjacent sequences: A292573 A292574 A292575 * A292577 A292578 A292579 KEYWORD nonn AUTHOR Guenther Schrack, Sep 19 2017 STATUS approved

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Last modified May 29 21:02 EDT 2024. Contains 372952 sequences. (Running on oeis4.)