Template:Noble Boolean functions/row sums

Template:Collapsible START The row sum of ${\mathrm{\Phi }}_n$ for $n\ge 1$ is $2^a\cdot (2^b-1)=2^{a+b}-2^a$ with $a=2^{n-1}$ and $b=2^n-1$.
That is a binary number consisting of $a$ 0s at the little and $b$ 1s at the big end.

E.g. that of ${\mathrm{\Phi }}_2$ is 0 + 6 + 8 + 14 = 28. (11100 as a binary number.)

n	sum of row n
0		1
1	$2^1\cdot (2^1-1)=2^2-2^1$	2
2	$2^2\cdot (2^3-1)=2^5-2^2$	28
3	$2^4\cdot (2^7-1)=2^{11}-2^4$	2032
4	$2^8\cdot (2^{15}-1)=2^{23}-2^8$	8388352
5	$2^{16}\cdot (2^{31}-1)=2^{47}-2^{16}$	140737488289792