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).
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.
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 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:
Difference between pairs of elements:
Compound relations:
a(n) = A284307(n+1) - 1 for n > 0.
Compositions:
KEYWORD
nonn
AUTHOR
Guenther Schrack, Sep 19 2017
STATUS
approved