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A062001
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Table by antidiagonals of n-Stohr sequences: T(n,k) is least positive integer not the sum of at most n distinct terms in the n-th row from T(n,1) through to T(n,k-1).
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3
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1, 2, 1, 3, 2, 1, 4, 4, 2, 1, 5, 7, 4, 2, 1, 6, 10, 8, 4, 2, 1, 7, 13, 15, 8, 4, 2, 1, 8, 16, 22, 16, 8, 4, 2, 1, 9, 19, 29, 31, 16, 8, 4, 2, 1, 10, 22, 36, 46, 32, 16, 8, 4, 2, 1, 11, 25, 43, 61, 63, 32, 16, 8, 4, 2, 1, 12, 28, 50, 76, 94, 64, 32, 16, 8, 4, 2, 1, 13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1
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OFFSET
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1,2
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LINKS
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FORMULA
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If k <= n+1 then A(n, k) = 2^(k-1), while if k > n+1, A(n, k) = (2^n - 1)*(k - n) + 1 (array).
T(n, k) = A(k, n-k+1) (antidiagonals).
T(2*n-1, n) = A000079(n-1), n >= 1.
T(2*n+1, n) = A000225(n+1), n >= 1.
T(2*n+3, n) = A036563(n+3), n >= 1.
T(n, k) = (2^k - 1)*(n-2*k+1) + 1 for k < n/2, otherwise 2^(n-k).
T(2*n+11, n) = A139697(n), n >= 1. (End)
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EXAMPLE
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Array begins as:
1, 2, 3, 4, 5, 6, 7, 8, 9, ... A000027;
1, 2, 4, 7, 10, 13, 16, 19, 22, ... A033627;
1, 2, 4, 8, 15, 22, 29, 36, 43, ... A026474;
1, 2, 4, 8, 16, 31, 46, 61, 76, ... A051039;
1, 2, 4, 8, 16, 32, 63, 94, 125, ... A051040;
1, 2, 4, 8, 16, 32, 64, 127, 190, ... ;
1, 2, 4, 8, 16, 32, 64, 128, 255, ... ;
1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
1, 2, 4, 8, 16, 32, 64, 128, 256, ... ;
Antidiagonal triangle begins as:
1;
2, 1;
3, 2, 1;
4, 4, 2, 1;
5, 7, 4, 2, 1;
6, 10, 8, 4, 2, 1;
7, 13, 15, 8, 4, 2, 1;
8, 16, 22, 16, 8, 4, 2, 1;
9, 19, 29, 31, 16, 8, 4, 2, 1;
10, 22, 36, 46, 32, 16, 8, 4, 2, 1;
11, 25, 43, 61, 63, 32, 16, 8, 4, 2, 1;
12, 28, 50, 76, 94, 64, 32, 16, 8, 4, 2, 1;
13, 31, 57, 91, 125, 127, 64, 32, 16, 8, 4, 2, 1;
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MATHEMATICA
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T[n_, k_]:= If[k<n/2, (2^k -1)*(n-2*k+1) +1, 2^(n-k)];
Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, May 03 2022 *)
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PROG
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(SageMath)
if (k<n/2): return (2^k -1)*(n-2*k+1) +1
else: return 2^(n-k)
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CROSSREFS
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A048483 can be seen as half this table.
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KEYWORD
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AUTHOR
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STATUS
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approved
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