A026533 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026519.

1, 3, 7, 18, 40, 104, 231, 607, 1353, 3575, 7989, 21169, 47384, 125757, 281798, 748638, 1678832, 4463098, 10014074, 26635050, 59787092, 159078450, 357193976, 950678416, 2135189511, 5684158586, 12769030254, 33999245582

Offset

0,2

Links

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

Formula

a(n) = Sum_{i=0..n} Sum_{j=0..i} A026519(i,j).

Mathematica

T[n_, k_]:= T[n, k]= If[k<0 || k>2*n, 0, If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k] ]]]]; (* T = A026519 *)
a[n_]:= a[n]= Block[{$RecursionLimit = Infinity}, Sum[T[i, j], {i, 0, n}, {j, 0, i}] ];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Dec 20 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k): # T = A026519
    if (k<0 or k>2*n): return 0
    elif (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n+1)//2
    elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
    else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
@CachedFunction
def a(n): return sum(sum( T(i, j) for j in (0..i)) for i in (0..n) )
[a(n) for n in (0..40)] # G. C. Greubel, Dec 20 2021

Crossrefs

Cf. A026519, A026520, A026521, A026522, A026523, A026524, A026525, A026526, A026527, A026528, A026529, A026530, A026531, A026534, A027262, A027263, A027264, A027265, A027266.

Sequence in context: A302408 A076700 A265007 * A131630 A305652 A356938

Adjacent sequences: A026530 A026531 A026532 * A026534 A026535 A026536

Keyword

nonn

Author

Clark Kimberling

Status

approved