A360292
a(n) = Sum_{k=0..floor(n/4)} binomial(n-1-3*k,k) * binomial(2*n-8*k,n-4*k).
Original entry on oeis.org
1, 2, 6, 20, 70, 254, 936, 3492, 13150, 49882, 190318, 729576, 2807816, 10841962, 41983588, 162973568, 633994982, 2471010742, 9646981054, 37718873700, 147676286078, 578883674722, 2271704404900, 8923807316892, 35087269756344, 138075819924306
Offset: 0
-
a(n) = sum(k=0, n\4, binomial(n-1-3*k, k)*binomial(2*n-8*k, n-4*k));
-
my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^4)))
A383573
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * binomial(2*(n-2*k),n-2*k).
Original entry on oeis.org
1, 2, 7, 24, 89, 338, 1311, 5152, 20449, 81778, 328999, 1330008, 5398265, 21984610, 89791103, 367643776, 1508560257, 6201927074, 25540266503, 105336838616, 435035342553, 1798875915826, 7446653956895, 30857577536800, 127987031688161, 531301328367762, 2207281722474919
Offset: 0
-
[&+[Binomial(n-k, k) * Binomial(2*(n-2*k), n-2*k): k in [0..Floor(n div 2)]]: n in [0..35]]; // Vincenzo Librandi, May 03 2025
-
Table[Sum[Binomial[n-k,k]* Binomial[2*(n-2*k),n-2*k],{k,0,Floor[n/2]}],{n,0,30}] (* Vincenzo Librandi, May 03 2025 *)
-
a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(2*(n-2*k), n-2*k));
A383581
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k,k) * binomial(2*(n-3*k),n-3*k).
Original entry on oeis.org
1, 2, 6, 21, 74, 270, 1005, 3788, 14418, 55289, 213270, 826614, 3216629, 12558928, 49175136, 193023965, 759299438, 2992534344, 11813985377, 46709675040, 184928644350, 733047010709, 2908981549006, 11555513379450, 45945148281437, 182835149061920, 728149606630164
Offset: 0
-
[&+[Binomial(n-2*k,k) * Binomial(2*(n-3*k),n-3*k): k in [0..n div 3]]: n in [0..25]]; // Vincenzo Librandi, May 02 2025
-
Table[Sum[Binomial[n-2*k,k]* Binomial[2*(n-3*k),n-3*k],{k,0,Floor[n/3]}],{n,0,30}] (* Vincenzo Librandi, May 02 2025 *)
-
a(n) = sum(k=0, n\3, binomial(n-2*k, k)*binomial(2*(n-3*k), n-3*k));
Showing 1-3 of 3 results.