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A262191 Number T(n,k) of compositions of n such that k is the maximal distance between two identical parts; triangle T(n,k), n>=2, 1<=k<=n-1, read by rows. 8
1, 0, 1, 3, 1, 1, 4, 4, 2, 1, 5, 6, 6, 3, 1, 12, 13, 12, 9, 4, 1, 21, 23, 25, 21, 13, 5, 1, 36, 42, 46, 46, 34, 18, 6, 1, 43, 68, 88, 92, 80, 52, 24, 7, 1, 88, 119, 152, 180, 172, 132, 76, 31, 8, 1, 133, 197, 267, 330, 352, 304, 208, 107, 39, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,4

LINKS

Alois P. Heinz, Rows n = 2..20, flattened

EXAMPLE

T(6,1) = 5: 33, 114, 411, 1122, 2211.

T(6,2) = 6: 141, 222, 1113, 1212, 2121, 3111.

T(6,3) = 6: 1131, 1221, 1311, 2112, 11112, 21111.

T(6,4) = 3: 11121, 11211, 12111.

T(6,5) = 1: 111111.

Triangle T(n,k) begins:

n\k:   1    2    3    4    5    6    7    8   9  10  11

---+----------------------------------------------------

02 :   1;

03 :   0,   1;

04 :   3,   1,   1;

05 :   4,   4,   2,   1;

06 :   5,   6,   6,   3,   1;

07 :  12,  13,  12,   9,   4,   1;

08 :  21,  23,  25,  21,  13,   5,   1;

09 :  36,  42,  46,  46,  34,  18,   6,   1;

10 :  43,  68,  88,  92,  80,  52,  24,   7,  1;

11 :  88, 119, 152, 180, 172, 132,  76,  31,  8,  1;

12 : 133, 197, 267, 330, 352, 304, 208, 107, 39,  9,  1;

MAPLE

b:= proc(n, s, l) option remember; `if`(n=0, 1, add(

      `if`(j in s, 0, b(n-j, s union {`if`(l=[], j, l[1])},

      `if`(l=[], [], [subsop(1=NULL, l)[], j]))), j=1..n))

    end:

T:= (n, k)-> b(n, {}, [0$k]) -b(n, {}, [0$(k-1)]):

seq(seq(T(n, k), k=1..n-1), n=2..14);

MATHEMATICA

b[n_, s_, l_] := b[n, s, l] = If[n==0, 1, Sum[If[MemberQ[s, j], 0, b[n-j, s ~Union~ {If[l=={}, j, l[[1]]]}, If[l=={}, {}, Append[Rest[l], j]]]], {j, 1, n}]]; T[n_, k_] := b[n, {}, Array[0&, k]] - b[n, {}, Array[0&, k-1]]; Table[T[n, k], {n, 2, 14}, { k, 1, n-1}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *)

CROSSREFS

Column k=1-5 gives A262192, A262194, A262196, A262197, A262200.

Row sums give A261982.

Cf. A261981.

Sequence in context: A335322 A171145 A271644 * A334844 A296457 A124020

Adjacent sequences:  A262188 A262189 A262190 * A262192 A262193 A262194

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 14 2015

STATUS

approved

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Last modified December 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)