A192655 -id:A192655 - cp's OEIS frontend

A192656 Partial sums of the Floor-Sqrt transform of central binomial coefficients.

1, 2, 4, 8, 16, 31, 61, 119, 232, 452, 881, 1720, 3364, 6588, 12921, 25375, 49891, 98198, 193461, 381464, 752740, 1486400, 2936951, 5806346, 11485043, 22728290, 44997518, 89121654, 176578446, 349977599, 693873777, 1376096873, 2729841361, 5416740769, 10750880013, 21342682400

Offset: 0

Emanuele Munarini, Jul 07 2011

nonn

Partial sums of A192655.

Table[Sum[Floor[Sqrt[Binomial[2k,k]]],{k,0,n}],{n,0,100}]

makelist(sum(floor(sqrt(binomial(2*k,k))),k,0,n),n,0,24);

a(n) = Sum_{k=0..n} floor(sqrt(binomial(2*k,k))).

A192658 Binomial convolution of the Floor-Sqrt transform of central binomial coefficients.

Original entry on oeis.org

1, 2, 6, 20, 72, 270, 1040, 4036, 15714, 61226, 238778, 930716, 3628520, 14143922, 55134174, 214941488, 838158510, 3269630046, 12761106790, 49834920864, 194743761948, 761543265544, 2980128724806, 11670402459630, 45734346816026, 179348093549914, 703781965002650

Offset: 0

Emanuele Munarini, Jul 07 2011

nonn

Cf. A000984, A192655.

Table[Sum[Binomial[n,k]Floor[Sqrt[Binomial[2k,k]]]Floor[Sqrt[Binomial[2n-2k,n-k]]],{k,0,n}],{n,0,100}]

makelist(sum(binomial(n,k)*floor(sqrt(binomial(2*k,k)))*floor(sqrt(binomial(2*n-2*k,n-k))),k,0,n),n,0,24);

a(n) = Sum_{k=0..n} binomial(n,k) * floor(sqrt(binomial(2*k,k))) * floor(sqrt(binomial(2*n-2*k,n-k))).

cp's OEIS Frontend

A192656 Partial sums of the Floor-Sqrt transform of central binomial coefficients.

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