A026598 a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026584.

1, 2, 6, 14, 37, 91, 234, 588, 1502, 3808, 9715, 24727, 63095, 160899, 410764, 1048598, 2678327, 6841725, 17482478, 44678724, 114205286, 291963048, 746504245, 1908907425, 4881860810, 12486083994, 31937825727, 81699259367

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(n) = Sum_{i=0..n} Sum_{j=0..i} A026584(i, j).

Conjecture: n*a(n) - (4*n-3)*a(n-1) - (2*n-3)*a(n-2) + 5*(4*n-9)*a(n-3) - 7*(n-3)*a(n-4) - 6*(4*n-15)*a(n-5) + 8*(2*n-9)*a(n-6) = 0. - R. J. Mathar, Jun 23 2013

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/2], If[EvenQ[n+k], T[n-1, k-2] + T[n-1, k], T[n-1, k-2] + T[n-1, k-1] + T[n-1, k] ]]]];
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 15 2021 *)

Prog

(Sage)
@CachedFunction
def T(n, k):  # T = A026584
    if (k==0 or k==2*n): return 1
    elif (k==1 or k==2*n-1): return (n//2)
    else: return T(n-1, k-2) + T(n-1, k) if ((n+k)%2==0) else T(n-1, k-2) + T(n-1, k-1) + T(n-1, k)
@CachedFunction
def A026598(n): return sum(sum(T(i, j) for j in (0..i)) for i in (0..n))
[A026598(n) for n in (0..40)] # G. C. Greubel, Dec 15 2021

Crossrefs

Cf. A026584, A026585, A026587, A026589, A026590, A026591, A026592, A026593, A026594, A026595, A026596, A026597, A026599, A027282, A027283, A027284, A027285, A027286.

Sequence in context: A144530 A248113 A339985 * A006864 A217420 A071636

Adjacent sequences: A026595 A026596 A026597 * A026599 A026600 A026601

Keyword

nonn

Author

Clark Kimberling

Status

approved