OFFSET
0,5
COMMENTS
This sequence is observed as the second difference in the expansion of 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^6)) (A029000), a sequence noted for its interlaced and structural coordination numbers.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,0,1,1,0,-1,-1).
FORMULA
a(n) = -a(n-1) + a(n-3) + a(n-4) + a(n-6) + a(n-7) - a(n-9) - a(n-10). a(6*k-2) = -a(6*k-1) = a(6*k) = k+1 for k >= 1.
G.f.: (x^9-x^7-x^6+x^4-x^3+x+1) / ((x-1)^2*(x+1)^2*(x^2-x+1)*(x^2+x+1)^2). - Colin Barker, May 24 2015
a(n) = -a(-14-n) for all n in Z. - Michael Somos, Jun 07 2015
EXAMPLE
G.f. = 1 + 2*x^4 - 2*x^5 + 2*x^6 + 3*x^10 - 3*x^11 + 3*x^12 + 4*x^16 + ...
MATHEMATICA
a[ n_] := With[ {m=n-1}, If[ OddQ[ Quotient[ m, 3]], Quotient[ m+9, 6] (-1)^Mod[m, 3], 0]]; (* Michael Somos, Jun 07 2015 *)
PROG
(PARI) Vec((x^9-x^7-x^6+x^4-x^3+x+1)/((x-1)^2*(x+1)^2*(x^2-x+1)*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, May 24 2015
(PARI) {a(n) = n--; if(n\3%2, (n+9)\6 * (-1)^(n%3), 0)}; /* Michael Somos, Jun 07 2015 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Avi Friedlich, May 21 2015
STATUS
approved