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

1, 0, 1, 0, 3, 0, 3, 0, 9, 1, 19, 2, 59, 13, 161, 50, 413, 123, 1201, 352, 3463, 689, 10921, 1585, 35365, 5409, 110773, 20950, 359725, 82702, 1192801, 320873, 3998397, 1096384, 13584075, 3417934, 45973713, 10657777, 157515581, 33447019, 543663919, 111463220

Offset: 1

Author

Reinhard Zumkeller, Feb 13 2013

Keywords

• nonn

Examples

			a(5) = 3: 5 = RMS(5) = RMS(1,7) = RMS(1,5,7);
a(7) = 3: 7 = RMS(7) = RMS(1,5,11) = RMS(1,5,7,11);
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);
a(10) = 1: 10 = RMS(1,3,5,7,9,11,15,17);
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);
a(12) = 2: 12 = RMS(1,5,7,9,11,15,17,19) = RMS(1,3,5,7,9,13,17,23).
		

Links

• Eric Weisstein's World of Math, Root-Mean-Square

Crossrefs

Cf. A000196, A005408, A163974, A164283.

Programs

Haskell

a211868 n = f a005408_list 1 nn 0 where
   f (o:os) l nl xx
     | yy > nl   = 0
     | yy < nl   = f os (l + 1) (nl + nn) yy + f os l nl xx
     | otherwise = if w == n then 1 else 0
     where w = if r == 0 then a000196 m else 0
           (m, r) = divMod yy l
           yy = xx + o * o
   nn = n ^ 2

Extensions

a(37)-a(40) from Alois P. Heinz, Feb 25 2013

a(41)-a(42) from Alois P. Heinz, May 03 2015