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A027067 a(n) = Sum_{k=n..2*n} T(n,k), T given by A027052. 3
1, 1, 4, 10, 27, 77, 220, 632, 1821, 5257, 15206, 44068, 127951, 372173, 1084382, 3164498, 9248241, 27064057, 79296978, 232597316, 682960523, 2007206245, 5904191878, 17380855190, 51203234981, 150943862857, 445250129556 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ 3^(n + 1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Nov 06 2019

MAPLE

T:= proc(n, k) option remember;

      if k=0 or k=2 or k=2*n then 1

    elif k=1 then 0

    else add(T(n-1, k-j), j=1..3)

      fi

    end:

seq( add(T(n, k), k=n..2*n), n=0..30); # G. C. Greubel, Nov 06 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n, k], {k, n, 2*n}], {n, 0, 30}] (* G. C. Greubel, Nov 06 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (k==0 or k==2 or k==2*n): return 1

    elif (k==1): return 0

    else: return sum(T(n-1, k-j) for j in (1..3))

[sum(T(n, k) for k in (n..2*n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

CROSSREFS

Sequence in context: A052982 A108672 A000495 * A050262 A295208 A222453

Adjacent sequences:  A027064 A027065 A027066 * A027068 A027069 A027070

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 24 13:05 EST 2020. Contains 332209 sequences. (Running on oeis4.)