cp's OEIS Frontend

A211868 Number of ways to write n as the root-mean-square (RMS) of a set of distinct odd integers.

%I A211868 #15 Feb 16 2025 08:33:17
%S A211868 1,0,1,0,3,0,3,0,9,1,19,2,59,13,161,50,413,123,1201,352,3463,689,
%T A211868 10921,1585,35365,5409,110773,20950,359725,82702,1192801,320873,
%U A211868 3998397,1096384,13584075,3417934,45973713,10657777,157515581,33447019,543663919,111463220
%N A211868 Number of ways to write n as the root-mean-square (RMS) of a set of distinct odd integers.
%H A211868 Eric Weisstein's World of Math, <a href="https://mathworld.wolfram.com/Root-Mean-Square.html">Root-Mean-Square</a>
%e A211868 a(5) = 3: 5 = RMS(5) = RMS(1,7) = RMS(1,5,7);
%e A211868 a(7) = 3: 7 = RMS(7) = RMS(1,5,11) = RMS(1,5,7,11);
%e A211868 a(9) = 9: 9 = RMS(9) = RMS(5,7,13) = RMS(5,7,9,13) = RMS(3,5,11,13) = RMS(3,5,9,11,13) = RMS(1,3,7,11,15) = RMS(1,3,7,9,11,15) = RMS(1,3,5,17) = RMS(1,3,5,9,17);
%e A211868 a(10) = 1: 10 = RMS(1,3,5,7,9,11,15,17);
%e A211868 a(11) = 19: 11 = RMS(11) = RMS(3,9,13,15) = RMS(3,9,11,13,15) = RMS(5,7,17) = RMS(5,7,11,17) = RMS(1,5,13,17) = RMS(1,5,11,13,17) = RMS(1,3,9,15,17) = RMS(1,3,9,11,15,17) = RMS(3,5,7,9,13,15,17) = RMS(3,5,7,9,11,13,15,17) = RMS(1,5,7,13,19) = RMS(1,5,7,11,13,19) = RMS(1,3,7,9,15,19) = RMS(1,3,7,9,11,15,19) = RMS(3,5,7,9,21) = RMS(3,5,7,9,11,21) = RMS(1,3,5,9,13,21) = RMS(1,3,5,9,11,13,21);
%e A211868 a(12) = 2: 12 = RMS(1,5,7,9,11,15,17,19) = RMS(1,3,5,7,9,13,17,23).
%o A211868 (Haskell)
%o A211868 a211868 n = f a005408_list 1 nn 0 where
%o A211868    f (o:os) l nl xx
%o A211868      | yy > nl   = 0
%o A211868      | yy < nl   = f os (l + 1) (nl + nn) yy + f os l nl xx
%o A211868      | otherwise = if w == n then 1 else 0
%o A211868      where w = if r == 0 then a000196 m else 0
%o A211868            (m, r) = divMod yy l
%o A211868            yy = xx + o * o
%o A211868    nn = n ^ 2
%Y A211868 Cf. A000196, A005408, A163974, A164283.
%K A211868 nonn
%O A211868 1,5
%A A211868 _Reinhard Zumkeller_, Feb 13 2013
%E A211868 a(37)-a(40) from _Alois P. Heinz_, Feb 25 2013
%E A211868 a(41)-a(42) from _Alois P. Heinz_, May 03 2015