A027272 Self-convolution of row n of array T given by A026552.

1, 3, 19, 58, 462, 1608, 13446, 48924, 417440, 1553940, 13409576, 50618184, 440013462, 1676640462, 14649846820, 56201554888, 492944907180, 1900789437276, 16721000706580, 64734185205960, 570792185166764, 2216888144737508, 19584623363041704, 76265067399850848

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A026552, A026553, A026554, A026555, A026556, A026557, A026558, A026559, A026560, A026563, A026564, A026566, A026567, A027273, A027274, A027275, A027276.

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+2)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k] + T[n-1, k-1], T[n-1, k-2] + T[n-1, k]]]]; (* T=A026552 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[n, k]*T[n, 2*n-k], {k, 0, 2*n}]];
Table[a[n], {n,0,40}] (* G. C. Greubel, Dec 18 2021 *)

Sage

@CachedFunction
def T(n,k): # T = A026552
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+2)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-2)
@CachedFunction
def a(n): return sum( T(n,k)*T(n,2*n-k) for k in (0..2*n) )
[a(n) for n in (0..40)] # G. C. Greubel, Dec 18 2021

Formula

a(n) = Sum_{k=0..2*n} A026552(n, k)*A026552(n, 2*n-k).

Extensions

More terms from Sean A. Irvine, Oct 26 2019