A174095
Triangle T(n,k,q) = Sum_{j=0..10} q^j * floor(A174093(n,k)/2^j) with q=1, read by rows.
Original entry on oeis.org
1, 1, 1, 1, 7, 1, 1, 7, 7, 1, 1, 7, 10, 7, 1, 1, 8, 11, 11, 8, 1, 1, 10, 18, 15, 18, 10, 1, 1, 11, 26, 19, 19, 26, 11, 1, 1, 15, 39, 38, 18, 38, 39, 15, 1, 1, 16, 53, 67, 31, 31, 67, 53, 16, 1, 1, 18, 70, 109, 67, 22, 67, 109, 70, 18, 1
Offset: 0
Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 7, 7, 1;
1, 7, 10, 7, 1;
1, 8, 11, 11, 8, 1;
1, 10, 18, 15, 18, 10, 1;
1, 11, 26, 19, 19, 26, 11, 1;
1, 15, 39, 38, 18, 38, 39, 15, 1;
1, 16, 53, 67, 31, 31, 67, 53, 16, 1;
1, 18, 70, 109, 67, 22, 67, 109, 70, 18, 1;
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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,1): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
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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, 1], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 10 2021 *)
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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,1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
A174096
Triangle T(n,k,q) = Sum_{j=0..10} q^j * floor(A174093(n,k)/2^j) with q=2, read by rows.
Original entry on oeis.org
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
Offset: 0
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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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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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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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
A174097
Triangle T(n,k,q) = Sum_{j=0..10} q^j * floor(A174093(n,k)/2^j) with q=3, read by rows.
Original entry on oeis.org
1, 1, 1, 1, 19, 1, 1, 19, 19, 1, 1, 19, 24, 19, 1, 1, 20, 25, 25, 20, 1, 1, 24, 70, 65, 70, 24, 1, 1, 25, 90, 71, 71, 90, 25, 1, 1, 65, 231, 230, 70, 230, 231, 65, 1, 1, 66, 295, 671, 211, 211, 671, 295, 66, 1, 1, 70, 684, 941, 671, 84, 671, 941, 684, 70, 1
Offset: 0
Triangle begins as:
1;
1, 1;
1, 19, 1;
1, 19, 19, 1;
1, 19, 24, 19, 1;
1, 20, 25, 25, 20, 1;
1, 24, 70, 65, 70, 24, 1;
1, 25, 90, 71, 71, 90, 25, 1;
1, 65, 231, 230, 70, 230, 231, 65, 1;
1, 66, 295, 671, 211, 211, 671, 295, 66, 1;
1, 70, 684, 941, 671, 84, 671, 941, 684, 70, 1;
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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,3): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
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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, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Feb 10 2021 *)
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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,3) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
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