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A174096
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Triangle T(n,k,q) = Sum_{j=0..10} q^j * floor(A174093(n,k)/2^j) with q=2, read by rows.
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4
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1, 1, 1, 1, 12, 1, 1, 12, 12, 1, 1, 12, 16, 12, 1, 1, 13, 17, 17, 13, 1, 1, 16, 36, 32, 36, 16, 1, 1, 17, 49, 37, 37, 49, 17, 1, 1, 32, 93, 92, 36, 92, 93, 32, 1, 1, 33, 124, 197, 80, 80, 197, 124, 33, 1, 1, 36, 204, 304, 197, 44, 197, 304, 204, 36, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Row sums are: 1, 2, 14, 26, 42, 62, 138, 208, 472, 870, 1528, ...
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LINKS
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FORMULA
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T(n, k, q) = Sum_{j=0..10} q^j * floor(A174093(n, k)/2^j), for q = 2.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 12, 1;
1, 12, 12, 1;
1, 12, 16, 12, 1;
1, 13, 17, 17, 13, 1;
1, 16, 36, 32, 36, 16, 1;
1, 17, 49, 37, 37, 49, 17, 1;
1, 32, 93, 92, 36, 92, 93, 32, 1;
1, 33, 124, 197, 80, 80, 197, 124, 33, 1;
1, 36, 204, 304, 197, 44, 197, 304, 204, 36, 1;
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MATHEMATICA
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A174093[n_, k_]:= If[n<2, 1, Binomial[n-k+1, k] + Binomial[k+1, n-k]];
T[n_, k_, q_]:= Sum[q^j*Floor[A174093[n, k]/2^j], {j, 0, 10}];
Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 10 2021 *)
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PROG
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(Sage)
def A174093(n, k): return 1 if n<2 else binomial(n-k+1, k) + binomial(k+1, n-k)
def T(n, k, q): return sum( q^j*(A174093(n, k)//2^j) for j in (0..10) )
flatten([[T(n, k, 2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
(Magma)
A174093:= func< n, k | n lt 2 select 1 else Binomial(n-k+1, k) + Binomial(k+1, n-k) >;
T:= func< n, k, q | (&+[ q^j*Floor(A174093(n, k)/2^j): j in [0..10]]) >;
[T(n, k, 2): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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