A381327 a(n) is the number of nonnegative integers that can be represented by n segments in the Cistercian numeral system.
1, 24, 214, 910, 2099, 2858, 2415, 1190, 289
Offset: 1
Links
- Daniel Carter Beard, The American boys' book of signs, signals and symbols. New York Public Library. Philadelphia: Lippincott. p. 92, 1918.
- dCode, Cistercian Monk Numerals
- Lauron William De Laurence, The Great Book of Magical Art, Hindu Magic and East Indian Occultism. Chicago: De Laurence Co. p. 174, 1915.
- Agrippa von Nettesheim and Heinrich Cornelius, De Occulta Philosophia, pp. CXLII - CXLIII, 1533 (in Latin).
- Wikipedia, Cistercian numerals.
Crossrefs
Cf. A341737.
Programs
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Mathematica
SN:={"0"->1, "1"->2, "2"->2, "3"->2, "4"->2, "5"->3, "6"->2, "7"->3, "8"->3, "9"->4}; OI:={11, 15, 17, 19, 22, 28, 29, 51, 55, 57, 59, 71, 75, 77, 79, 82, 88, 89, 91, 92, 95, 97, 98, 99}; a[k_]:=Count[Table[(Characters[IntegerString[Floor[n/100]]]/. SN//Total)-Length[Characters[IntegerString[Floor[n/100]]]]+1-If[MemberQ[OI, Floor[n/100]], 1, 0]-Boole[Floor[n/100]==99]+(Characters[IntegerString[Mod[n, 100]]]/. SN//Total)-Length[Characters[IntegerString[Mod[n, 100]]]]+1-If[MemberQ[OI, Mod[n, 100]], 1, 0]-Boole[Mod[n, 100]==99]-1, {n, 0, 9999}],k]; Array[a,9]
Formula
Sum_{k=1..9} a(k) = 10^4.
Comments