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A247976 Triangle read by rows: T(n,k) generated by m-gon expansions in the case of odd m with "vertex to vertex" version or even m with "vertex to side" version. (See comment for details.) 3
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 4, 6, 4, 1, 4, 6, 4, 1, 4, 6, 4, 1, 4, 6, 4, 1, 5, 10, 10, 5, 1, 5, 10, 10, 5, 1, 5, 10, 10, 5, 1, 5, 10, 10, 5, 1, 6, 15, 20, 15, 6, 1, 6, 15, 20, 15, 6, 1, 6, 15, 20, 15, 6, 1, 6, 15, 20, 15, 6, 1, 7, 21 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Refer to triangle expansions in A061777 and A101946 (and their companions for m-gons) which are "vertex to vertex" and "vertex to side" versions respectively. The label values at each iteration can be arranged as triangle. Any m-gon can also be arranged as the same triangle with conditions: (i) m is odd and expansion is "vertex to vertex" version or (ii) m is even and expansion is "vertex to side" version. m*Sum_{i=1..k}T(n,k) gives the total label value in n-th iteration. See illustration.

LINKS

Table of n, a(n) for n=1..87.

Kival Ngaokrajang, Illustration of initial terms

EXAMPLE

Triangle begins:

1

1  1

1  1  2

1  2  1  2

1  2  1  3  3

1  3  3  1  3  3

1  3  3  1  4  6  4

1  4  6  4  1  4  6  4

1  4  6  4  1  5 10 10  5

1  5 10 10  5  1  5 10 10  5

...

PROG

(Small Basic)

a[1][1]=1

a[2][1]=1

a[2][2]=1

TextWindow.Write(1+", "+1+", "+1+", ")

for n=3 To 30

  If Math.Remainder(n, 2)=1 then

    '===========odd n=================

    j=1

    for k=1 To n

      If k <= (n/2+1/2) then

         a[n][k]=a[n-1][k]

       Else

         a[n][k]=a[n][j]+a[n][j+1]

         j=j+1

       EndIf

       TextWindow.Write(a[n][k]+", ")

     EndFor

  else

    '==============even n===============

    For k=1 To n

      If k <=1 Then

        a[n][k]=1

      Else

        If k < n/2+1 then

          a[n][k]=a[n-1][k-1]+a[n-1][k]

        Else

          a[n][k]=a[n][k-n/2]

        EndIf

      EndIf

      TextWindow.Write(a[n][k]+", ")

    EndFor

  EndIf

EndFor

CROSSREFS

Rows sum: A027383.

Column (start from 1s): c3=A008805, c4=A058187, c5=A000332 repeated, c6=A000389 repeated, c7=A000579 repeated.

Vertex to vertex: A061777, A247618, A247619, A247620.

Vertex to side: A101946, A247903, A247904, A247905.

Cf. A074909.

Sequence in context: A161261 A161286 A185216 * A280986 A344773 A103689

Adjacent sequences:  A247973 A247974 A247975 * A247977 A247978 A247979

KEYWORD

tabl,nonn

AUTHOR

Kival Ngaokrajang, Sep 28 2014

STATUS

approved

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Last modified August 5 20:11 EDT 2021. Contains 346488 sequences. (Running on oeis4.)