

A117695


a(n) is the number of pairs of distinct positive integers not containing a digit 0 giving a sum equal to n.


1



0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 9, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 12, 12, 13, 13, 14, 14, 15, 15, 16, 18, 16, 16, 17, 17, 18, 18, 19, 19, 20, 22, 20, 20, 21, 21, 22, 22, 23, 23, 24, 27, 24, 24, 25, 25, 26, 26, 27, 27, 28, 31, 28, 28, 29, 29, 30, 30, 31
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OFFSET

1,5


LINKS



EXAMPLE

10 = 1 + 9 = 2 + 8 = 3 + 7 = 4 + 6 therefore we have 4 different couples.
9 + 1 is not considered because it is the same couple as 1 + 9.
5 + 5 is not considered because we consider couples with different numbers.


MAPLE

P:=proc(n)local i, j, k, cc, lm, ok, count; for cc from 1 by 1 to n do if trunc(cc/2)*2=cc then lm:=cc/21 else lm:=trunc(cc/2) fi; count:=0; for i from 1 by 1 to lm do ok:=0; k:=i; while k>0 do j:=frac(k/10)*10; if j=0 then ok:=1; fi; k:=trunc(k/10); od; k:=cci; while k>0 do j:=frac(k/10)*10; if j=0 then ok:=1; fi; k:=trunc(k/10); od; if ok=1 then count:=count+1; fi; od; print(lmcount); od; end: P(1000);


PROG

(PARI) iszerofree(n) = vecmin(digits(n)) > 0
a(n) = sum(i = 1, (n1)\2, iszerofree(i) && iszerofree(ni)) \\ David A. Corneth, May 12 2024


CROSSREFS



KEYWORD

nonn,base,changed


AUTHOR



EXTENSIONS



STATUS

approved



