A143458 Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=7.

1, 4, 7, 10, 13, 16, 19, 22, 25, 37, 58, 88, 127, 175, 232, 298, 373, 484, 658, 922, 1303, 1828, 2524, 3418, 4537, 5989, 7963, 10729, 14638, 20122, 27694, 37948, 51559, 69526, 93415, 125602, 169516, 229882, 312964, 426808, 581485, 790063, 1070308, 1447114

Offset

0,2

Comments

a(n) is also the number of length n quaternary words with at least 7 0-digits between any other digits.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

Formula

G.f.: 1/(x^7*(1-x-3*x^8)).

a(0)=1, a(1)=4, a(2)=7, a(3)=10, a(4)=13, a(5)=16, a(6)=19, a(7)=22, a(n)=a(n-1)+3*a(n-8). - Harvey P. Dale, Jul 22 2013

Maple

a := proc(k::nonnegint) local n, i, j; if k=0 then unapply (4^n, n) else unapply ((Matrix(k+1, (i, j)-> if (i=j-1) or j=1 and i=1 then 1 elif j=1 and i=k+1 then 3 else 0 fi)^(n+k))[1, 1], n) fi end(7): seq (a(n), n=0..60);

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 3}, {1, 4, 7, 10, 13, 16, 19, 22}, 50] (* Harvey P. Dale, Jul 22 2013 *)

Crossrefs

7th column of A143461.

Sequence in context: A338701 A310679 A143459 * A004084 A121381 A310680

Adjacent sequences: A143455 A143456 A143457 * A143459 A143460 A143461

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 16 2008

Status

approved