A027040 a(n) = self-convolution of row n of array T given by A027023.

1, 3, 9, 31, 129, 531, 2129, 8351, 32177, 122211, 458801, 1706015, 6293169, 23057651, 83992313, 304424639, 1098525761, 3948727555, 14145206209, 50515602111, 179904080257, 639103899411, 2265253438745, 8012421964063

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..2*n} T(n,k)*T(n,2*n-k), where T = A027023. - G. C. Greubel, Nov 05 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)*T(n, 2*n-k), k=0..2*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]*T[n, 2*n-k], {k, 0, 2*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)*T(n, 2*n-k) for k in (0..2*n)) for n in (4..30)] # G. C. Greubel, Nov 05 2019

Crossrefs

Sequence in context: A071603 A349970 A090595 * A111063 A245116 A377959

Adjacent sequences: A027037 A027038 A027039 * A027041 A027042 A027043

Keyword

nonn

Author

Clark Kimberling

Status

approved