A242182 Numbers with four C's in Roman numerals.

390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 1390, 1391, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 1890, 1891, 1892, 1893, 1894, 1895, 1896, 1897, 1898, 1899, 2390, 2391, 2392, 2393, 2394, 2395, 2396

Offset

1,1

Comments

These will always have CCCXC in them.

Links

Table of n, a(n) for n=1..47.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Formula

From Elmo R. Oliveira, Jul 02 2026: (Start)

a(n) = a(n-1) + a(n-10) - a(n-11) for n > 11.

G.f.: x*(390+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+101*x^10) / (1-x-x^10+x^11) = x*(390 - 389*x + 100*x^10 - 101*x^11) / ((1-x) * (-1+x)^2 * (1+x) * (1-x+x^2-x^3+x^4) * (1+x+x^2+x^3+x^4)). (End)

Example

390 = CCCXC; 890 = DCCCXC.

Mathematica

Select[Range[2000], StringCount[RomanNumeral[#], "C"]==4&] (* Harvey P. Dale, Jul 30 2015 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 890}, 40] (* Harvey P. Dale, Jul 30 2015 *)

Prog

(PARI) lista() = {for (i=0, 9, for (j=0, 9, print1((390+j)+500*i, ", "); ); ); } \\ Michel Marcus, May 14 2014

Crossrefs

Sequence in context: A299719 A300340 A228580 * A136153 A379532 A069477

Adjacent sequences: A242179 A242180 A242181 * A242183 A242184 A242185

Keyword

nonn,easy,less,base,changed

Author

J. Lowell, May 06 2014

Extensions

More terms from Elmo R. Oliveira, Jul 02 2026

Status

approved