[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A082874
Independence number of king KG_4 on triangle board B_n.
2
1, 3, 5, 9, 14, 18, 26, 34, 41, 52, 64, 72, 87, 102, 113, 131, 150, 162, 184, 206, 221, 246, 272, 288, 317, 346, 365, 397, 430, 450, 486, 522, 545, 584, 624, 648, 691, 734, 761, 807, 854, 882, 932, 982, 1013, 1066, 1120, 1152, 1209, 1266
OFFSET
1,2
LINKS
J.-J. Bode, H. Harborth and M. Harborth, King independence on triangle boards, Discr. Math., 266 (2003), 101-107.
FORMULA
a(n)= a(n-1) +a(n-3) -a(n-4) +a(n-6) -a(n-7) -a(n-9) +a(n-10), n>12.
G.f.: x*(x^11 -x^10 -x^8 -x^7 -3*x^6 -2*x^5 -3*x^4 -3*x^3 -2*x^2 -2*x -1) / ((x -1)^3*(x +1)*(x^2 -x +1)*(x^2 +x +1)^2). - Colin Barker, Aug 06 2014
MAPLE
A082874 := proc(n)
if n = 1 then
1;
elif n = 2 then
3;
else
m := modp(n, 6) ;
3*n^2+op(m+1, [0, n+2, 2*n-4, 3, n+2, 2*n-1]) ;
%/6 ;
end if ;
end proc:
seq(A082874(n), n=1..50) ; # R. J. Mathar, Aug 05 2014
PROG
(Magma) I:=[1, 3, 5, 9, 14, 18, 26, 34, 41, 52, 64, 72]; [n le 12 select I[n] else Self(n-1)+Self(n-3)-Self(n-4)+Self(n-6)-Self(n-7)-Self(n-9)+Self(n-10): n in [1..60]]; // Vincenzo Librandi, Aug 06 2014
(PARI) Vec(x*(x^11-x^10-x^8-x^7-3*x^6-2*x^5-3*x^4-3*x^3-2*x^2-2*x-1)/((x-1)^3*(x+1)*(x^2-x+1)*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Aug 06 2014
CROSSREFS
Cf. A082873.
Sequence in context: A288259 A355489 A372639 * A266250 A127720 A118002
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 25 2003
STATUS
approved