A026643 a(n) = A026637(n, floor(n/2)).

1, 1, 2, 4, 8, 13, 26, 46, 92, 166, 332, 610, 1220, 2269, 4538, 8518, 17036, 32206, 64412, 122464, 244928, 467842, 935684, 1794196, 3588392, 6903352, 13806704, 26635774, 53271548, 103020253, 206040506, 399300166, 798600332

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Links

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

Crossrefs

Cf. A026637, A026638, A026639, A026640, A026641, A026642, A026644.

Cf. A026966, A026967, A026968, A026969, A026970.

Programs

Magma

[1] cat [n le 4 select 2^(n-1) else (4*Self(n-1) +(7*n-9)*Self(n-2) +2*Self(n-3) +4*(n-1)*Self(n-4))/(2*(n+1)): n in [1..40]]; // G. C. Greubel, Jul 01 2024

Mathematica

T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[(3*n -1)/2], T[n-1,k-1] + T[n-1,k] ]]; (* A026637 *)
A026643[n_]:= T[n, Floor[n/2]];
Table[A026643[n], {n,0,40}] (* G. C. Greubel, Jul 01 2024 *)

SageMath

@CachedFunction
def a(n): # a = A026643
    if n<5: return (1,1,2,4,8)[n]
    else: return (4*a(n-1) +(7*n-9)*a(n-2) +2*a(n-3) +4*(n-1)*a(n-4))/(2*(n+1))
[a(n) for n in range(41)] # G. C. Greubel, Jul 01 2024

Formula

a(n) = (4*a(n-1) + (7*n-9)*a(n-2) + 2*a(n-3) + 4*(n-1)*a(n-4))/(2*(n+1)) with a(0) = a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8. - G. C. Greubel, Jul 01 2024