OFFSET
0,6
COMMENTS
Column 1 of A118897.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..3501
Omar Khadir, László Németh, and László Szalay, Tiling of dominoes with ranked colors, Results in Math. (2024) Vol. 79, Art. No. 253. See p. 2.
László Németh and László Szalay, Explicit solution of system of two higher-order recurrences, arXiv:2408.12196 [math.NT], 2024. See p. 10.
Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1,-4,-3,-2,-1).
FORMULA
G.f.: z^4/(1-z-z^2-z^3-z^4)^2.
From Bobby Milazzo, Aug 30 2009: (Start)
a(1)=0,a(2)=0,a(3)=0,a(4)=1,a(5)=2,a(6)=5,a(7)=12,a(8)=28
a(n) = 2a(n-1)+a(n-2)-a(n-4)-4a(n-5)-3a(n-6)-2a(n-7)-a(n-8). (End)
EXAMPLE
a(6)=5 because we have 000010,000011,010000,100001 and 110000.
G.f. = x^4 + 2*x^5 + 5*x^6 + 12*x^7 + 28*x^8 + 62*x^9 + ... - Zerinvary Lajos, Jun 02 2009
MAPLE
g:=z^4/(1-z-z^2-z^3-z^4)^2: gser:=series(g, z=0, 40): seq(coeff(gser, z, n), n=0..37);
MATHEMATICA
RecurrenceTable[{a[1]==0, a[2]==0, a[3]==0, a[4]==1, a[5]==2, a[6]==5, a[7]==12, a[8]==28, a[n]==2a[n-1]+a[n-2]-a[n-4]-4a[n-5]-3a[n-6]-2a[n-7]-a[n-8]}, a, {n, 9, 50}] (* Bobby Milazzo, Aug 30 2009 *)
LinearRecurrence[{2, 1, 0, -1, -4, -3, -2, -1}, {0, 0, 0, 0, 1, 2, 5, 12}, 50] (* Harvey P. Dale, Aug 01 2012 *)
PROG
(Sage) taylor( mul(x/(1-x-x^2-x^3-x^4)^2 for i in range(1, 2)), x, 0, 31)# Zerinvary Lajos, Jun 02 2009
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, May 04 2006
STATUS
approved