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A027037 Diagonal sum of left-justified array T given by A027023. 2
1, 1, 2, 3, 3, 6, 7, 11, 16, 21, 33, 48, 65, 101, 146, 203, 311, 450, 635, 963, 1396, 1989, 2993, 4348, 6233, 9329, 13574, 19543, 29135, 42446, 61303, 91123, 132884, 192377, 285309, 416384, 603925, 894069, 1305618, 1896495, 2803611, 4096182, 5957183, 8796287 (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) = Sum_{k=0..n} A027023(n-k, k). - Sean A. Irvine, Oct 22 2019

MAPLE

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

      if n<0 or k>2*n then 0

    elif 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, k), k=0..n), n=0..30); # G. C. Greubel, Nov 05 2019

MATHEMATICA

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

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (n<0 or k>2*n): return 0

    elif (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, k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Nov 05 2019

CROSSREFS

Sequence in context: A028249 A121833 A091606 * A276428 A020878 A158278

Adjacent sequences:  A027034 A027035 A027036 * A027038 A027039 A027040

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Sean A. Irvine, Oct 21 2019

STATUS

approved

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Last modified May 6 17:50 EDT 2021. Contains 343586 sequences. (Running on oeis4.)