A027040 - OEIS

%I #11 Nov 06 2019 22:35:48

%S 1,3,9,31,129,531,2129,8351,32177,122211,458801,1706015,6293169,

%T 23057651,83992313,304424639,1098525761,3948727555,14145206209,

%U 50515602111,179904080257,639103899411,2265253438745,8012421964063

%N a(n) = self-convolution of row n of array T given by A027023.

%H G. C. Greubel, <a href="/A027040/b027040.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = Sum_{k=0..2*n} T(n,k)*T(n,2*n-k), where T = A027023. - _G. C. Greubel_, Nov 05 2019

%p T:= proc(n, k) option remember;

%p       if (n<0 or k>2*n) then 0

%p     elif k<3 or k=2*n then 1

%p     else add(T(n-1, k-j), j=1..3)

%p       fi

%p     end:

%p seq( add(T(n,k)*T(n,2*n-k), k=0..2*n), n=0..30); # _G. C. Greubel_, Nov 05 2019

%t 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 *)

%o (Sage)

%o @CachedFunction

%o def T(n, k):

%o     if (n<0 or k>2*n): return 0

%o     elif (k<3 or k==2*n): return 1

%o     else: return sum(T(n-1, k-j) for j in (1..3))

%o [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

%K nonn

%O 0,2

%A _Clark Kimberling_