A026964 - OEIS

%I #12 Jun 23 2024 18:37:06

%S 1,12,77,434,1978,8830,37409,156474,644305,2632506,10684360,43166246,

%T 173768764,697596990,2794438513,11174809302,44626341136,178018744896,

%U 709505830530,2825762505810,11247704919634,44749537493028,177970696795672,707580176408854,2812524327414647

%N a(n) = Sum_{k=0..n-3} T(n,k) * T(n,k+3), with T given by A026626.

%H G. C. Greubel, <a href="/A026964/b026964.txt">Table of n, a(n) for n = 3..1000</a>

%t T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[3*n/2], T[n-1,k-1] +T[n-1,k]]]; (* T = A026626 *)

%t A262964[n_]:= Sum[T[n,k]*T[n,k+3], {k,0,n-3}];

%t Table[A262964[n], {n,3,40}] (* _G. C. Greubel_, Jun 23 2024 *)

%o (SageMath)

%o @CachedFunction

%o def T(n, k): # T = A026626

%o     if (k==0 or k==n): return 1

%o     elif (k==1 or k==n-1): return int(3*n//2)

%o     else: return T(n-1, k-1) + T(n-1, k)

%o def A262964(n): return sum( T(n,k)*T(n,k+3) for k in range(n-2))

%o [A262964(n) for n in range(3,41)] # _G. C. Greubel_, Jun 23 2024

%Y Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.

%Y Cf. A026633, A026634, A026635, A026636, A026961, A026962, A026963.

%Y Cf. A026965.

%K nonn

%O 3,2

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Oct 20 2019