A160020 Row sums of triangle in A160019 .

1, 4, 4, 16, 10, 18, 22, 64, 46, 46, 58, 76, 88, 94, 106, 256, 214, 198, 226, 196, 288, 246, 274, 312, 436, 370, 406, 388, 484, 438, 466, 1024, 934, 886, 946, 820, 1072, 934, 994, 808, 1348, 1186, 1254, 1012, 1396, 1126, 1186, 1264, 1996, 1786, 1870, 1516, 2044

Offset: 0

Author

Philippe Deléham, Apr 29 2009

Keywords

• easy
• nonn

Examples

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

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

Programs

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

PARI

a(n)={my(b=2^hammingweight(n)); b^2 + (n+1-b)*(n-b)} \\ Andrew Howroyd, Feb 02 2020

Formula

a(n) = b^2 + (n+1-b)*(n-b), where b = 2^A000120(n). - Andrew Howroyd, Feb 02 2020

Extensions

Terms a(11) and beyond from Andrew Howroyd, Feb 02 2020