A082874 Independence number of king KG_4 on triangle board B_n.

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

Table of n, a(n) for n=1..50.

J.-J. Bode, H. Harborth and M. Harborth, King independence on triangle boards, Discr. Math., 266 (2003), 101-107.

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), 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

Adjacent sequences: A082871 A082872 A082873 * A082875 A082876 A082877

Keyword

nonn,easy

Author

N. J. A. Sloane, May 25 2003

Status

approved