A026540 a(n) = T(n,n-3), T given by A026536. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.

1, 2, 6, 16, 36, 104, 215, 635, 1275, 3786, 7518, 22344, 44170, 131264, 259002, 769578, 1517418, 4508580, 8888495, 26412001, 52077234, 154773696, 305257251, 907432695, 1790353357, 5323519838, 10507386918, 31251588060

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A026536.

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], 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[T[n,n-3], {n,3,40}] (* G. C. Greubel, Apr 10 2022 *)

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 A026540(n): return T(n,n-3)
[A026540(n) for n in (3..40)] # G. C. Greubel, Apr 10 2022

Formula

a(n) = A026536(n, n-3).