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

1,5

Links

Table of n, a(n) for n=1..42.

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

Example

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).

Prog

(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

Crossrefs

Cf. A000196, A005408, A163974, A164283.

Sequence in context: A055945 A138123 A328382 * A127372 A350950 A051171

Adjacent sequences: A211865 A211866 A211867 * A211869 A211870 A211871

Keyword

nonn

Author

Reinhard Zumkeller, Feb 13 2013

Extensions

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

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

Status

approved