A027268 a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A026536.

0, 6, 20, 180, 644, 5502, 20292, 174456, 654632, 5673140, 21528000, 187675644, 717800628, 6284986554, 24178479500, 212408191568, 820811282352, 7229648901024, 28037230854096, 247468885359240, 962488105227160, 8510025522045036, 33177800527098040, 293772371437293720

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Formula

a(n) = Sum_{k=0..2n-1} A026536(n,k) * A026536(n,k+1)

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[n/2], If[EvenQ[n], T[n-1, k-2] +T[n-1, k-1] +T[n-1, k], T[n-1, k-2] +T[n-1, k]] ]];
Table[Sum[T[n, k]*T[n, k+1], {k, 0, 2*n-1}], {n, 40}] (* G. C. Greubel, Apr 12 2022 *)

Prog

(SageMath)
@CachedFunction
def T(n, k): # A026536
    if k < 0 or n < 0: return 0
    elif k == 0 or k == 2*n: return 1
    elif k == 1 or k == 2*n-1: return n//2
    elif n % 2 == 1: return T(n-1, k-2) + T(n-1, k)
    return T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
def A027268(n): return sum(T(n, k)*T(n, k+1) for k in (0..2*n-1))
[A027268(n) for n in (1..40)] # G. C. Greubel, Apr 12 2022

Crossrefs

Cf. A026536, A027267, A027269.

Sequence in context: A332391 A027148 A095854 * A000388 A347919 A227769

Adjacent sequences: A027265 A027266 A027267 * A027269 A027270 A027271

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 26 2019

Status

approved