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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 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.)