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A027038 Diagonal sum of right-justified array T given by A027023. 2
1, 1, 2, 5, 7, 18, 43, 103, 264, 687, 1809, 4836, 13049, 35493, 97218, 267857, 741791, 2063574, 5763595, 16155403, 45429488, 128121191, 362287433, 1026918632, 2917313257, 8304598593, 23685134746, 67669857661, 193652803391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..750

FORMULA

a(n) = Sum_{k=0..n} T(n-k, 2*n-3*k), where T = A027023. - G. C. Greubel, Nov 05 2019

MAPLE

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

      if k<3 or k=2*n then 1

    else add(T(n-1, k-j), j=1..3)

      fi

    end:

seq( add(T(n-k, 2*n-3*k), k=0..n), n=0..30); # G. C. Greubel, Nov 05 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k<3 || k==2*n, 1, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n-k, 2*n-3*k], {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Nov 05 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (k<3 or k==2*n): return 1

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

[sum(T(n-k, 2*n-3*k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 05 2019

CROSSREFS

Sequence in context: A247323 A099357 A306918 * A341322 A173929 A173299

Adjacent sequences:  A027035 A027036 A027037 * A027039 A027040 A027041

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 6 17:45 EDT 2021. Contains 343586 sequences. (Running on oeis4.)