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
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
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 13 2010
STATUS
approved