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A026589 a(n) = T(n,n-4), T given by A026584. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4. 17
1, 2, 9, 22, 69, 178, 497, 1294, 3452, 8964, 23430, 60556, 156663, 403214, 1037191, 2660978, 6821200, 17459732, 44657246, 114117628, 291449047, 743904326, 1897956899, 4840429962, 12340947855, 31455453822, 80158533099 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

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

FORMULA

a(n) = A026584(n, n-4).

Conjecture: -(n+4)*(65*n-269)*a(n) +(-65*n^2+140*n+1933)*a(n-1) +(809*n^2-2431*n-4514)*a(n-2) +(-123*n^2+2496*n-205)*a(n-3) +2*(-726*n^2+3737*n-4395)*a(n-4) +8*(56*n-215)*(2*n-9)*a(n-5) = 0. - 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-4], {n, 4, 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-4) for n in (4..40)] # G. C. Greubel, Dec 12 2021

CROSSREFS

Cf. A026584, A026585, A026587, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026598, A026599, A027282, A027283, A027284, A027285, A027286.

Sequence in context: A086718 A023625 A166754 * A319792 A091002 A330419

Adjacent sequences:  A026586 A026587 A026588 * A026590 A026591 A026592

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified January 25 11:49 EST 2022. Contains 350567 sequences. (Running on oeis4.)