A026587 a(n) = T(n, n-2), T given by A026584. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=2.

1, 1, 5, 9, 28, 62, 167, 399, 1024, 2518, 6359, 15819, 39759, 99427, 249699, 626203, 1573524, 3953446, 9943905, 25019005, 62994733, 158680545, 399936573, 1008438757, 2543992514, 6420413940, 16210331727, 40943722115, 103453402718

Offset

2,3

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Formula

a(n) = A026584(n, n-2).

Conjecture: (n+2)*a(n) = (3*n+2)*a(n-1) +(3*n+2)*a(n-2) -(11*n-16)*a(n-3) -2*(n-3)*a(n-4) +4*(2*n-9)*a(n-5). - R. J. Mathar, Jun 23 2013

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+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]; (* T = A026584 *)
Table[T[n, n-2], {n, 2, 40}] (* G. C. Greubel, Dec 12 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k): # T = A026584
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n//2)
    else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
[T(n, n-2) for n in (2..40)] # G. C. Greubel, Dec 12 2021

Crossrefs

Cf. A026584, A026585, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.

Sequence in context: A272315 A301747 A193316 * A147367 A147230 A192914

Adjacent sequences: A026584 A026585 A026586 * A026588 A026589 A026590

Keyword

nonn

Author

Clark Kimberling

Status

approved