A137713 - OEIS

%I #6 Aug 20 2018 16:47:05

%S 1,2,3,5,7,12,18,30,48,78,126,205,331,536,868,1404,2272,3676,5948,

%T 9624,15572,25195,40767,65962,106729,172690,279419,452109,731528,

%U 1183637,1915165,3098802,5013967,8112769,13126737,21239506,34366243,55605749,89971992,145577742,235549734,381127476,616677210

%N Row sums of triangle A137712.

%C a(n)/a(n-1) tends to phi.

%H Robert Israel, <a href="/A137713/b137713.txt">Table of n, a(n) for n = 1..1000</a>

%e a(6) = 12 = sum of row 6 terms of triangle A137712: (8 + 2 + 1 + 0 + 0 + 1).

%p for n from 1 to 100 do

%p   T[n,1]:= combinat:-fibonacci(n);

%p   for k from 2 to n do

%p     if n >= 2*k-1 then T[n,k]:= T[n-1,k-1] - T[n-k,k-1]

%p     else T[n,k]:= T[n-1,k-1]

%p     fi

%p   od:

%p od:

%p seq(add(T[n,k],k=1..n),n=1..100); # _Robert Israel_, Aug 20 2018

%Y Cf. A137712.

%K nonn

%O 1,2

%A _Gary W. Adamson_, Feb 08 2008

%E Corrected and extended by _Robert Israel_, Aug 20 2018