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A027040
a(n) = self-convolution of row n of array T given by A027023.
2
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
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 A255382
KEYWORD
nonn
STATUS
approved