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A174097
Triangle T(n,k,q) = Sum_{j=0..10} q^j * floor(A174093(n,k)/2^j) with q=3, read by rows.
4
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
0,5
COMMENTS
Row sums are: 1, 2, 21, 40, 64, 92, 255, 374, 1124, 2488, 4818, ...
FORMULA
T(n, k, q) = Sum_{j=0..10} q^j * floor(A174093(n, k)/2^j), for q = 3.
EXAMPLE
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;
MATHEMATICA
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 *)
PROG
(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, 3) 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, 3): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
CROSSREFS
Cf. A174093 (q=0), A174095 (q=1), A174096 (q=2), this sequence (q=3).
Sequence in context: A040363 A040362 A040361 * A174040 A176078 A022182
KEYWORD
nonn,tabl,easy,less
AUTHOR
Roger L. Bagula, Mar 07 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 10 2021
STATUS
approved