A026557 - OEIS

A026557

a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.

1, 3, 12, 28, 93, 201, 631, 1316, 4037, 8259, 25052, 50680, 152782, 306958, 921982, 1844304, 5526849, 11024331, 32987492, 65675764, 196323853, 390374193, 1166171943, 2316881892, 6918228187, 13737041045, 41007165500

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OFFSET

4,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 4..1000

FORMULA

a(n) = A026552(n, n-4).

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 *)

Table[T[n, n-4], {n, 4, 40}] (* G. C. Greubel, Dec 17 2021 *)

PROG

(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)

[T(n, n-4) for n in (4..40)] # G. C. Greubel, Dec 17 2021

CROSSREFS