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

0,2

Links

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

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A319070 A227074 A174595 * A273370 A273830 A250069

Adjacent sequences: A160017 A160018 A160019 * A160021 A160022 A160023

Keyword

easy,nonn

Author

Philippe Deléham, Apr 29 2009

Extensions

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

Status

approved