A215415 a(2*n) = n, a(4*n+1) = 2*n-1, a(4*n+3) = 2*n+3.
0, -1, 1, 3, 2, 1, 3, 5, 4, 3, 5, 7, 6, 5, 7, 9, 8, 7, 9, 11, 10, 9, 11, 13, 12, 11, 13, 15, 14, 13, 15, 17, 16, 15, 17, 19, 18, 17, 19, 21, 20, 19, 21, 23, 22, 21, 23, 25, 24, 23, 25, 27, 26, 25, 27, 29, 28, 27, 29, 31, 30, 29, 31, 33, 32, 31, 33, 35, 34, 33, 35, 37
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
Programs
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Mathematica
Flatten[Table[{2n, 2n - 1, 2n + 1, 2n + 3}, {n, 0, 19}]] (* Alonso del Arte, Aug 09 2012 *) -
PARI
a(n) = ((-3*I)*((-I)^n-I^n)+2*n)/4 \\ Colin Barker, Oct 19 2015
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PARI
concat(0, Vec(-x*(1-3*x+x^2)/((x^2+1)*(x-1)^2) + O(x^100))) \\ Colin Barker, Oct 19 2015
Formula
a(2*n) = n, a(2*n+1) = A097062(n+1).
a(3*n) =3*A004525(n).
a(n) = +2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4).
G.f. -x*(1-3*x+x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Aug 11 2012
a(n) = ((-3*I)*((-I)^n-I^n)+2*n)/4. - Colin Barker, Oct 19 2015
Comments