This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A305556 Irregular triangle read by rows: T(n,k) is the number of superdiagonal bargraphs with area n and with k columns. 2
 1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 1, 5, 3, 1, 6, 6, 1, 7, 10, 1, 8, 15, 1, 1, 9, 21, 4, 1, 10, 28, 10, 1, 11, 36, 20, 1, 12, 45, 35, 1, 13, 55, 56, 1, 1, 14, 66, 84, 5, 1, 15, 78, 120, 15, 1, 16, 91, 165, 35, 1, 17, 105, 220, 70, 1, 18, 120, 286, 126, 1, 19, 136, 364, 210, 1, 1, 20, 153, 455 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Emeric Deutsch, Emanuele Munarini, Simone Rinaldi, Skew Dyck paths, area, and superdiagonal bargraphs, Journal of Statistical Planning and Inference, Vol. 140, Issue 6, June 2010, pp. 1550-1562. FORMULA T(n,k) = binomial(n-1-k*(k-1)/2,k-1), 1<=k <= (sqrt(1+8*n)-1)/2. EXAMPLE 1,    1,    1,   1,    1,   2,    1,   3,    1,   4,   1,    1,   5,   3,    1,   6,   6,    1,   7,  10,    1,   8,  15,   1,    1,   9,  21,   4,    1,  10,  28,  10,    1,  11,  36,  20,    1,  12,  45,  35,    1,  13,  55,  56,   1,    1,  14,  66,  84,   5,    1,  15,  78, 120,  15,    1,  16,  91, 165,  35,    1,  17, 105, 220,  70,    1,  18, 120, 286, 126,    1,  19, 136, 364, 210,   1,    1,  20, 153, 455, 330,   6,    1,  21, 171, 560, 495,  21,    1,  22, 190, 680, 715,  56,    1,  23, 210, 816,1001, 126,    1,  24, 231, 969,1365, 252,    1,  25, 253,1140,1820, 462,    1,  26, 276,1330,2380, 792,   1,    1,  27, 300,1540,3060,1287,   7,    1,  28, 325,1771,3876,2002,  28, MAPLE A305556 := proc(n, k)     binomial(n-binomial(k, 2)-1, k-1) ; end proc: for n from 0 to 30 do for k from 1 to floor((sqrt(1+8*n)-1)/2) do     printf("%d, ", A305556(n, k)) ; end do: end do: CROSSREFS Cf. A219282 (row sums), A000217 (column 3), A000292 (column 4), A000332 (column 5) Sequence in context: A142593 A226248 A102547 * A177812 A280504 A087267 Adjacent sequences:  A305553 A305554 A305555 * A305557 A305558 A305559 KEYWORD nonn,tabf,easy AUTHOR R. J. Mathar, Jun 21 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 03:54 EDT 2019. Contains 327210 sequences. (Running on oeis4.)