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A211868 Number of ways to write n as the root-mean-square (RMS) of a set of distinct odd integers. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A051171 A300904

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

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Last modified January 27 02:46 EST 2020. Contains 331291 sequences. (Running on oeis4.)