A360291
a(n) = Sum_{k=0..floor(n/3)} binomial(n-1-2*k,k) * binomial(2*n-6*k,n-3*k).
Original entry on oeis.org
1, 2, 6, 20, 72, 264, 984, 3714, 14148, 54284, 209482, 812196, 3161340, 12345658, 48348522, 189807336, 746740510, 2943359208, 11620961412, 45950375602, 181936110006, 721233025332, 2862271873966, 11370584735100, 45212101270728, 179926167512914
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(n-1-2*k, k)*binomial(2*n-6*k, n-3*k));
-
my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^3)))
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));
A383582
a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*(n-4*k),n-4*k).
Original entry on oeis.org
1, 2, 6, 20, 71, 256, 942, 3512, 13221, 50138, 191260, 733088, 2821037, 10892100, 42174848, 163706656, 636816019, 2481902842, 9689155902, 37882580356, 148313102097, 581365577564, 2281393560802, 8961689897248, 35235582858441, 138657185501870, 546064549476476
Offset: 0
-
[&+[Binomial(n-3*k,k) * Binomial(2*(n-4*k),n-4*k): k in [0..n div 4]]: n in [0..45]]; // Vincenzo Librandi, May 02 2025
-
Table[Sum[Binomial[n-3*k,k]* Binomial[2*(n-4*k),n-4*k],{k,0,Floor[n/4]}],{n,0,30}] (* Vincenzo Librandi, May 02 2025 *)
-
a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(2*(n-4*k), n-4*k));
Showing 1-3 of 3 results.