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A175331 Array A092921(n,k) without the first two rows, read by antidiagonals. 4
1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 4, 2, 1, 1, 8, 7, 4, 2, 1, 1, 13, 13, 8, 4, 2, 1, 1, 21, 24, 15, 8, 4, 2, 1, 1, 34, 44, 29, 16, 8, 4, 2, 1, 1, 55, 81, 56, 31, 16, 8, 4, 2, 1, 1, 89, 149, 108, 61, 32, 16, 8, 4, 2, 1, 1, 144, 274, 208, 120, 63, 32, 16, 8, 4, 2, 1, 1, 233, 504, 401, 236, 125, 64, 32, 16, 8, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=2..92.

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

T(n,k) = A092921(n,k), n >= 2.

T(n,2) = A000045(n).

T(n,3) = A000073(n+2).

T(n,4) = A000078(n+2).

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:

A175331 := proc(n, k) A092921(n, k) ; end proc: # R. J. Mathar, Dec 17 2010

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

Cf. A000045, A048887, A048004, A126198.

Sequence in context: A152462 A180360 A318805 * A098805 A168396 A049286

Adjacent sequences:  A175328 A175329 A175330 * A175332 A175333 A175334

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Dec 03 2010

STATUS

approved

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Last modified June 25 04:18 EDT 2019. Contains 324346 sequences. (Running on oeis4.)