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A026745
a(n) = Sum_{j=0..n} Sum_{i=0..n} T(j,i), T given by A026736.
1
1, 3, 7, 15, 32, 66, 139, 285, 599, 1227, 2577, 5277, 11075, 22671, 47543, 97287, 203860, 417006, 873175, 1785513, 3736210, 7637604, 15972143, 32641221, 68224004, 139389570, 291199307, 594818781, 1242097912, 2536656174
OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..2000 (terms 0..1000 from G. C. Greubel)
FORMULA
a(n) ~ c * phi^(3*n/2), where c = 1/2 + 3*phi^2 / (2*sqrt(5)) if n is even, c = 3*phi^(5/2) / (2*sqrt(5)) if n is odd and phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jul 22 2019
MATHEMATICA
T[n_, k_]:= T[n, k] = If[k==0 || k==n, 1, If[EvenQ[n] && k==(n-2)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k]]];
b[n_]:= Sum[T[n, j], {j, 0, n}]; Table[Sum[b[j], {j, 0, n}], {n, 0, 35}] (* G. C. Greubel, Jul 22 2019 *)
PROG
(Sage)
@CachedFunction
def T(n, k):
if (k==0 or k==n): return 1
elif (mod(n, 2)==0 and k==(n-2)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
else: return T(n-1, k-1) + T(n-1, k)
def b(n): return sum(T(n, j) for j in (0..n))
[sum(b(j) for j in (0..n)) for n in (0..35)] # G. C. Greubel, Jul 22 2019
CROSSREFS
Cf. A026736.
Sequence in context: A336976 A368346 A117079 * A139333 A099444 A374678
KEYWORD
nonn
STATUS
approved