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2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 7, 5, 8, 5, 7, 11, 11, 10, 10, 11, 11, 21, 16, 21, 12, 21, 16, 21, 36, 36, 28, 28, 28, 28, 36, 36, 71, 57, 64, 36, 56, 36, 64, 57, 71, 127, 127, 93, 93, 72, 72, 93, 93, 127, 127, 253, 211, 220, 130, 165, 90, 165, 130, 220, 211, 253
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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G. C. Greubel, Rows n = 0..100 of triangle, flattened
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FORMULA
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Sum_{k=0..n} T(n,k) = 2^(n+1).
T(n, k) = binomial(n, floor((n+1 - (-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)). - G. C. Greubel, Jan 31 2020
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EXAMPLE
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Triangle begins:
2;
2, 2;
3, 2, 3;
4, 4, 4, 4;
7, 5, 8, 5, 7;
11, 11, 10, 10, 11, 11;
21, 16, 21, 12, 21, 16, 21;
36, 36, 28, 28, 28, 28, 36, 36;
71, 57, 64, 36, 56, 36, 64, 57, 71; ...
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MAPLE
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seq(seq( binomial(n, floor((n+1-(-1)^(n-k)*(k+1))/2)) +binomial(n, floor(k/2)), k=0..n), n=0..12); # G. C. Greubel, Jan 31 2020
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MATHEMATICA
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T[n_, k_]= Binomial[n, Floor[(n+1 -(-1)^(n-k)*(k+1))/2]] + Binomial[n, Floor[k/2]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 31 2020 *)
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PROG
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(PARI) T(n, k) = binomial(n, (n+1 -(-1)^(n-k)*(k+1))\2 ) + binomial(n, k\2); \\ G. C. Greubel, Jan 31 2020
(Magma) [Binomial(n, Floor((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Floor(k/2)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 31 2020
(Sage) [[binomial(n, floor((n+1 -(-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 31 2020
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, Int((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Int(k/2)) ))); # G. C. Greubel, Jan 31 2020
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CROSSREFS
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Cf. A061554, A107430.
Sequence in context: A143976 A194296 A194336 * A025128 A058769 A194312
Adjacent sequences: A127156 A127157 A127158 * A127160 A127161 A127162
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe Deléham, Mar 25 2007
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STATUS
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approved
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