A117695 a(n) is the number of pairs of distinct positive integers not containing a digit 0 giving a sum equal to n.

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

Offset

1,5

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

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/2-1 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:=cc-i; 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(lm-count); od; end: P(1000);

Prog

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

Crossrefs

Cf. A117644.

Sequence in context: A074796 A061070 A285879 * A375502 A074794 A234309

Adjacent sequences: A117692 A117693 A117694 * A117696 A117697 A117698

Keyword

nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 13 2006

Extensions

Name edited and offset changed to 1 by David A. Corneth, May 12 2024

Status

approved