OFFSET
0,3
COMMENTS
When A064861 is regarded as a triangle read by rows, this is [1,0,-1,0,0,0,0,0,0,...] DELTA [2,-1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Dec 14 2008
LINKS
Reinhard Zumkeller, Rows n = 0..125 of table, flattened
Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.
Milan Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From N. J. A. Sloane, Feb 13 2013
Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5.
C. de Jesús Pita Ruiz Velasco, Convolution and Sulanke Numbers, JIS 13 (2010) 10.1.8.
R. A. Sulanke, Problem 10894, Amer. Math. Monthly 108, (2001), p. 770.
FORMULA
G.f.: Sum_{m>=0} Sum_{n>=0} a_{m, n}*t^m*s^n = A(t,s) = (1+2*t+s)/(1-2*t^2-s^2-3*s*t).
EXAMPLE
Table begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
2, 3, 5, 6, 8, 9, 11, ...
2, 8, 13, 25, 33, 51, ...
4, 12, 38, 63, 129, ...
4, 28, 66, 192, ...
MAPLE
MATHEMATICA
max = 12; se = Series[(1 + 2*x + y*x)/(1 - 2*x^2 - y^2*x^2 - 3*y*x^2), {x, 0, max}, {y, 0, max}]; cc = CoefficientList[se, {x, y}]; Flatten[ Table[ cc[[n, k]], {n, 1, max}, {k, n, 1, -1}]] (* Jean-François Alcover, Oct 21 2011, after g.f. *)
PROG
(PARI) a(n, m)=if(n<0 || m<0, 0, polcoeff(polcoeff((1+2*x+y*x)/(1-2*x^2-y^2*x^2-3*y*x^2)+O(x^(n+m+1)), n+m), m))
(Haskell)
a064861 n k = a064861_tabl !! n !! k
a064861_row n = a064861_tabl !! n
a064861_tabl = map fst $ iterate f ([1], 2) where
f (xs, z) = (zipWith (+) ([0] ++ map (* z) xs) (xs ++ [0]), 3 - z)
-- Reinhard Zumkeller, May 01 2014
CROSSREFS
KEYWORD
AUTHOR
Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10 2001
STATUS
approved