A199921 Number of Roman numerals < 4000 with n letters.

7, 31, 93, 215, 389, 573, 691, 691, 573, 389, 215, 93, 31, 7, 1

Offset

1,1

Comments

Note that the sequence is completely symmetrical with the addition of the single (notional) Roman string of length zero. - Ian Duff, Jun 27 2017

Links

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Roman Numerals.

Wikipedia, Roman numerals

Example

a(1) = 7, since there are the seven one-letter roman numerals I, V, X, L, C, D, M.
a(15) = 1, since there is one fifteen-letter roman numeral MMMDCCCLXXXVIII.

Maple

for i from 1 to 15 do L[i]:={}: od: for n from 1 to 3999 do L[length(convert(n, roman))]:={op(L[length(convert(n, roman))]), n}; od:
seq(nops(L[i]), i=1..15); # Martin Renner, Nov 13 2011

Mathematica

romanLetterCount = Table[0, {15}]; j = 1; While[j < 4000, romanLetterCount[[StringLength[IntegerString[j, "Roman"]]]]++; j++]; romanLetterCount (* Alonso del Arte, Nov 12 2011 *)
Rest[BinCounts[StringLength[RomanNumeral[Range[3999]]]]] (* Paolo Xausa, Mar 19 2024 *)

Prog

(Haskell)
import Data.List (group, sort)
a199921 n = a199921_list !! (n-1)
a199921_list = map length $ group $ sort $ map (a055642 . a061493) [1..3999]
-- Reinhard Zumkeller, Apr 14 2013

Crossrefs

Cf. A003587, A006968.

Cf. A055642, A061493.

Sequence in context: A226838 A205801 A193437 * A192596 A055899 A218956

Adjacent sequences: A199918 A199919 A199920 * A199922 A199923 A199924

Keyword

nonn,fini,full

Author

Martin Renner, Nov 12 2011

Status

approved