A027069 a(n) = diagonal sum of left-justified array T given by A027052.

1, 1, 1, 2, 2, 4, 5, 7, 11, 14, 22, 32, 43, 67, 97, 134, 206, 298, 419, 637, 923, 1312, 1978, 2872, 4111, 6161, 8961, 12888, 19232, 28010, 40423, 60129, 87665, 126840, 188216, 274634, 398151, 589689, 861001, 1250210, 1848840, 2700900, 3926839, 5799949, 8476579

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=0..n} A027052(n - k, k). - Sean A. Irvine, Oct 22 2019

Maple

T:= proc(n, k) option remember;
      if k<0 or k>2*n then 0
    elif 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), k=0..n), n=0..50); # G. C. Greubel, Nov 06 2019

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, 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], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Nov 06 2019 *)

Prog

(Sage)
@CachedFunction
def T(n, k):
    if (k<0 or k>2*n): return 0
    elif (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, k) for k in (0..n)) for n in (0..50)] # G. C. Greubel, Nov 06 2019

Crossrefs

Sequence in context: A034398 A277062 A355638 * A238494 A359388 A325550

Adjacent sequences: A027066 A027067 A027068 * A027070 A027071 A027072

Keyword

nonn

Author

Clark Kimberling

Extensions

More terms from Sean A. Irvine, Oct 22 2019

Status

approved