A160020 - OEIS

%I #7 Feb 02 2020 22:23:11

%S 1,4,4,16,10,18,22,64,46,46,58,76,88,94,106,256,214,198,226,196,288,

%T 246,274,312,436,370,406,388,484,438,466,1024,934,886,946,820,1072,

%U 934,994,808,1348,1186,1254,1012,1396,1126,1186,1264,1996,1786,1870,1516,2044

%N Row sums of triangle in A160019 .

%H Andrew Howroyd, <a href="/A160020/b160020.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = b^2 + (n+1-b)*(n-b), where b = 2^A000120(n). - _Andrew Howroyd_, Feb 02 2020

%e Triangle A160019 begins : 1 ; 1,3 ; 1,0,3 ; 1,3,5,7 ; 1,0,2,4,3 ; 1,3,0,2,5,7 ; ...

%o (PARI) \\ here S(n,k) is A047999.S(n,k)={bitand(n-k, k)==0}a(n)={my(b=0); sum(k=0, n, if(S(n,k), b++; 2*b-1, 2*(k-b)))} \\ _Andrew Howroyd_, Feb 02 2020

%o (PARI) a(n)={my(b=2^hammingweight(n)); b^2 + (n+1-b)*(n-b)} \\ _Andrew Howroyd_, Feb 02 2020

%Y Cf. A000120, A001316, A007318, A047999, A160019.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Apr 29 2009

%E Terms a(11) and beyond from _Andrew Howroyd_, Feb 02 2020