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A130856
The digital root (A010888) of the Catalan numbers A000108.
3
1, 1, 2, 5, 5, 6, 6, 6, 8, 2, 2, 7, 4, 4, 9, 9, 9, 6, 6, 6, 3, 3, 3, 9, 9, 9, 8, 2, 2, 4, 1, 1, 3, 3, 3, 1, 7, 7, 2, 5, 5, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 6, 6, 6, 3, 3, 3, 9, 9, 9, 3, 3, 3, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8, 2, 2, 4, 1, 1, 3
OFFSET
0,3
LINKS
MAPLE
A130856 := proc(n) option remember: if(n=0)then return 1:fi: return ((add(procname(k)*procname(n-1-k), k=0..n-1)-1) mod 9) + 1 end: seq(A130856(n), n=0..100); # Nathaniel Johnston, May 05 2011
MATHEMATICA
droot[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]; droot/@CatalanNumber[ Range[ 0, 100]] (* Harvey P. Dale, Apr 09 2022 *)
PROG
(PARI) a(n) = (binomial(2*n, n)/(n+1)-1)%9 + 1; \\ Michel Marcus, Nov 28 2022
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
N. J. A. Sloane, Aug 21 2007
EXTENSIONS
Name corrected by Nathaniel Johnston, May 05 2011
STATUS
approved