OFFSET
0,15
COMMENTS
Row sums of number triangle A124749.
Let A(n) denote the n X n matrix with 1's along and everywhere above the main diagonal, 1's along the sub-sub-subdiagonal, and 0's everywhere else; for n>3, a(n) equals (-1)^(n+1) times the sum of the coefficients of the characteristic polynomial of A(n-3) (see Mathematica code below). - John M. Campbell, Mar 10 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,1,-1).
FORMULA
G.f.: (1 + x + x^2)/(1 - x^3 + x^4).
a(n) = Sum_{k=0..n} binomial(floor(k/3), n-k) * (-1)^(n-k).
a(n) = a(n-3) - a(n-4). - Wesley Ivan Hurt, May 02 2021
MATHEMATICA
A[n_] := Array[Sum[KroneckerDelta[#1, #2 - j], {j, 0, n}] + KroneckerDelta[#1, #2 + 3] &, {n, n}]; Table[(-1)^(r + 1)*Total[CoefficientList[CharacteristicPolynomial[A[r - 3], x], x]], {r, 4, 60}] (* John M. Campbell, Mar 10 2012 *)
CoefficientList[Series[(1+x+x^2)/(1-x^3+x^4), {x, 0, 70}], x] (* or *) LinearRecurrence[{0, 0, 1, -1}, {1, 1, 1, 1}, 70] (* Harvey P. Dale, Jun 06 2018 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 06 2006
STATUS
approved