login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259975 Irregular triangle read by rows: T(n,k) = number of ways of placing n balls into k boxes in such a way that any two adjacent boxes contain at least 4 balls. 3
1, 1, 1, 1, 1, 5, 1, 1, 6, 4, 1, 7, 9, 1, 8, 16, 1, 9, 25, 15, 1, 1, 10, 35, 40, 8, 1, 11, 46, 76, 31, 1, 12, 58, 124, 85, 1, 13, 71, 185, 190, 35, 1, 1, 14, 85, 260, 360, 154, 13, 1, 15, 100, 350, 610, 424, 76, 1, 16, 116, 456, 956, 930, 295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

R. P. Boas & N. J. A. Sloane, Correspondence, 1974

D. R. Breach, Letter to N. J. A. Sloane, Jun 1980

M. Hayes (proposer) and D. R. Breach (solver), A combinatorial problem, Problem 68-16, SIAM Rev. 12 (1970), 294-297.

EXAMPLE

Triangle begins:

  1;

  1;

  1;

  1;

  1,  5,   1;

  1,  6,   4;

  1,  7,   9;

  1,  8,  16;

  1,  9,  25,  15,   1;

  1, 10,  35,  40,   8;

  1, 11,  46,  76,  31;

  1, 12,  58, 124,  85;

  1, 13,  71, 185, 190,  35,  1;

  1, 14,  85, 260, 360, 154, 13;

  1, 15, 100, 350, 610, 424, 76;

  ...

MAPLE

b:= proc(n, v) option remember; expand(`if`(n=0,

      `if`(v=0, 1+x, 1), add(x*b(n-j, max(0, 4-j)), j=v..n)))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n, 0)):

seq(T(n), n=0..20);  # Alois P. Heinz, Jul 12 2015

MATHEMATICA

b[n_, v_] := b[n, v] = Expand[If[n == 0, If[v == 0, 1+x, 1], Sum[x*b[n-j, Max[0, 4-j]], {j, v, n}]]]; T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][b[n, 0]]; Table[T[n], {n, 0, 20}] // Flatten (* Jean-Fran├žois Alcover, Feb 13 2016, after Alois P. Heinz *)

CROSSREFS

Columns: A004120, A005337, A005338, A005339, A005340.

Row sums give A257666.

Sequence in context: A209575 A159570 A280374 * A028313 A173119 A050178

Adjacent sequences:  A259972 A259973 A259974 * A259976 A259977 A259978

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jul 12 2015

EXTENSIONS

More terms from Alois P. Heinz, Jul 12 2015

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)