A127804 - OEIS

%I #14 Feb 12 2024 08:25:35

%S 1,3,4,11,16,36,64,139,256,528,1024,2084,4096,8256,16384,32907,65536,

%T 131328,262144,524816,1048576,2098176,4194304,8390692,16777216,

%U 33558528,67108864,134225984,268435456

%N a(2n)=4^n, a(4*n+3)-(2^(4*n+3)+2^(2*n+1))=a(n).

%C Row sums of number triangle A127803.

%H R. J. Mathar, <a href="/A127804/b127804.txt">Table of n, a(n) for n = 0..61</a>

%F Conjecture: a(n) = 1 + A187767(n+1). - _Andrew Howroyd_, Jun 02 2017

%p A127804 := proc(n)

%p     add( A127803(n,k),k=0..n) ;

%p end proc: # _R. J. Mathar_, Feb 12 2024

%t rows = 30;

%t A[n_, k_] := If[k <= n, If[n <= 2 k, 1/(2*2^n - 1), 0], 0];

%t T = Table[A[n, k], {n, 0, rows-1}, {k, 0, rows-1}] // Inverse;

%t a[n_] := T[[n+1]] // Total;

%t Table[a[n], {n, 0, rows-1}] (* _Jean-François Alcover_, Jul 03 2018 *)

%Y Cf. A127803, A187767.

%K nonn

%O 0,2

%A _Paul Barry_, Jan 29 2007