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A026598
a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026584.
17
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
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
KEYWORD
nonn
STATUS
approved