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A158821
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Triangle read by rows: row n (n>=0) ends with 1, and for n>=1 begins with n; other entries are zero.
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8
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1, 1, 1, 2, 0, 1, 3, 0, 0, 1, 4, 0, 0, 0, 1, 5, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 1, 7, 0, 0, 0, 0, 0, 0, 1, 8, 0, 0, 0, 0, 0, 0, 0, 1, 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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G. C. Greubel, Rows n = 0..50 of the triangle, flattened
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FORMULA
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T(n, k) = A145677(n, n-k-1). - R. J. Mathar, Apr 01 2009
From G. C. Greubel, Dec 22 2021: (Start)
Sum_{k=0..n} T(n, k) = A000027(n).
Sum_{k=0..floor(n/2)} T(n-k, k) = A109613(n). (End)
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EXAMPLE
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Triangle begins:
1;
1, 1;
2, 0, 1;
3, 0, 0, 1;
4, 0, 0, 0, 1;
5, 0, 0, 0, 0, 1;
6, 0, 0, 0, 0, 0, 1;
7, 0, 0, 0, 0, 0, 0, 1;
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MAPLE
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A158821:= proc(n, k)
if n = k then 1;
elif k = 0 then n;
else 0;
end if;
end proc: # R. J. Mathar, Jan 08 2015
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MATHEMATICA
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T[n_, k_]:= If[k==0, Boole[n==0] +n, If[k==n, 1, 0]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Dec 22 2021 *)
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PROG
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(Sage)
def A158821(n, k):
if (k==0): return n + bool(n==0)
elif (k==n): return 1
else: return 0
flatten([[A158821(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Dec 22 2021
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CROSSREFS
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Cf. A000027, A109613, A145677.
Sequence in context: A309576 A128132 A127701 * A004199 A062283 A136493
Adjacent sequences: A158818 A158819 A158820 * A158822 A158823 A158824
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson, Mar 30 2008
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STATUS
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approved
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