OFFSET
2,5
COMMENTS
Antidiagonal sums are A048888. This is a transposed version of A048887, so the bivariate generating function is obtained by swapping the two arguments.
Brlek et al. (2006) call this table "number of psp-polyominoes with flat bottom". - N. J. A. Sloane, Oct 30 2018
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 125, 155.
LINKS
Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon, Tilings by translation: enumeration by a rational language approach, The Electronic Journal of Combinatorics, vol.13, (2006). Table 1 is essentially this array. - N. J. A. Sloane, Jul 20 2014
FORMULA
EXAMPLE
The array starts in row n=2 with columns k >= 1 as:
1 1 1 1 1 1 1 1 1 1
1 2 2 2 2 2 2 2 2 2
1 3 4 4 4 4 4 4 4 4
1 5 7 8 8 8 8 8 8 8
1 8 13 15 16 16 16 16 16 16
1 13 24 29 31 32 32 32 32 32
1 21 44 56 61 63 64 64 64 64
1 34 81 108 120 125 127 128 128 128
1 55 149 208 236 248 253 255 256 256
MAPLE
A092921 := proc(n, k) if k <= 0 or n <= 0 then 0; elif k = 1 or n = 1 then 1; else add( procname(n-i, k), i=1..k) ; end if; end proc:
MATHEMATICA
f[x_, n_] = (x - x^(m + 1))/(1 - 2*x + x^(m + 1))
a = Table[Table[SeriesCoefficient[
Series[f[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 1, 10}];
Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}];
Flatten[%]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Dec 03 2010
STATUS
approved