A226940 a(0)=0; if a(n-1) is odd, a(n) = n + a(n-1), otherwise a(n) = n - a(n-1).

0, 1, 3, 6, -2, 7, 13, 20, -12, 21, 31, 42, -30, 43, 57, 72, -56, 73, 91, 110, -90, 111, 133, 156, -132, 157, 183, 210, -182, 211, 241, 272, -240, 273, 307, 342, -306, 343, 381, 420, -380, 421, 463, 506, -462, 507, 553, 600, -552, 601, 651, 702, -650, 703, 757

Offset

0,3

Links

Table of n, a(n) for n=0..54.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Formula

G.f.: x*(1 +3*x +6*x^2 -2*x^3 +4*x^4 +4*x^5 +2*x^6 -6*x^7 +3*x^8 +x^9)/((1-x)^3*(1+x)^3*(1+x^2)^3). [Bruno Berselli, Jul 01 2013]

a(n) = 3*a(n-4) -3*a(n-8) +a(n-12). [Bruno Berselli, Jul 01 2013]

a(4n) = -A002939(n), a(4n+1) = A054569(n+1), a(4n+2) = A054554(n+2), a(4n+3) = A068377(n+2). [Bruno Berselli, Jul 02 2013]

Mathematica

LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {0, 1, 3, 6, -2, 7, 13, 20, -12, 21, 31, 42}, 60] (* Bruno Berselli, Jul 01 2013 *)

Prog

(Magma) [IsZero(n) select 0 else IsOdd(Self(n)) select n+Self(n) else n-Self(n): n in [0..60]]; // Bruno Berselli, Jul 01 2013
(Maxima) makelist(coeff(taylor(x*(1+3*x+6*x^2-2*x^3+4*x^4+4*x^5+2*x^6-6*x^7+3*x^8+x^9)/((1-x)^3*(1+x)^3*(1+x^2)^3), x, 0, n), x, n), n, 0, 60); /* Bruno Berselli, Jul 01 2013 */

Crossrefs

Cf. A081348 (second bisection); A002939, A054554, A054569, A068377.

Sequence in context: A339192 A171884 A339557 * A098141 A175458 A356080

Adjacent sequences: A226937 A226938 A226939 * A226941 A226942 A226943

Keyword

sign,easy

Author

Enrico Santilli, Jun 23 2013

Extensions

More terms from Bruno Berselli, Jul 01 2013

Status

approved