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A051340
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A simple 2-dimensional array, read by antidiagonals.
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30
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1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A member of the accumulation chain
...< A051340 < A141419 < A185874 < A185875 < A185876 < ...
(See A144112 for the definition of accumulation array.)
In the mth accumulation array of A051340,
(row 1)=C(m,1) and (column 1)=C(1,m+1), for m>=0.
[From Clark Kimberling, ck6(AT)evansville.edu, Feb 5 2011]
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REFERENCES
| A. V. Mikhalev and A. A. Nechaev, Linear recurring sequences over modules, Acta Applic. Math., 42 (1996), 161-202.
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FORMULA
| For n>0, a(n(n+3)/2)=n if k is not of form n*(n+3)/2 a(k)=1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 31 2002
T(n,1)=n and T(n,k)=1 if k>1, for n>=1. [From Clark Kimberling, ck6(AT)evansville.edu, Feb 5 2011]
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EXAMPLE
| Northwest corner:
1...1...1...1...1...1...1
3...1...1...1...1...1...1
4...1...1...1...1...1...1
5...1...1...1...1...1...1
6...1...1...1...1...1...1
The Mathematica code show that the weight array of A051340 (i.e., the array of which A051340 is the accumulation array, has northwest corner
1....0...0...0...0...0...0
1...-1...0...0...0...0...0
1...-1...0...0...0...0...0
1...-1...0...0...0...0...0
1...-1...0...0...0...0...0
[From Clark Kimberling, ck6(AT)evansville.edu, Feb 5 2011]
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MATHEMATICA
| (* This program generates A051340, then its accumulation array A141419, then its weight array described under Example. *)
f[n_, 0]:=0; f[0, k_]:=0; (* needed for the weight array *)
f[n_, 1]:=n; f[n_, k_]:=1/; k>1;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A051340 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* A141419 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
w[m_, n_]:=f[m, n]+f[m-1, n-1]-f[m, n-1]-f[m-1, n]/; Or[m>0, n>0];
TableForm[Table[w[n, k], {n, 1, 10}, {k, 1, 15}]] (* weight array *)
Table[w[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
[From Clark Kimberling, ck6(AT)evansville.edu, Feb 5 2011]
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CROSSREFS
| Cf. A144112, A141419, A185874, A185875, A185876.
Sequence in context: A080209 A127949 A167407 * A165430 A164823 A167269
Adjacent sequences: A051337 A051338 A051339 * A051341 A051342 A051343
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KEYWORD
| easy,nice,nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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