A169973 - OEIS

%I #7 Mar 30 2012 17:38:11

%S 1,1,1,2,2,4,7,13,26,51,52,103,154,205,256,308,359,410,461,512,2408,

%T 4814,20276,70298,189440,427728,855452,1583464,2833460,5127424,

%U 10197920,20395832,42204112,86360168,173465856,345264448,687194480

%N a(n) = number of ways to write n as a sum of distinct numbers <= n, where the addition is carryless mod 10.

%C a(0) = 1 by convention, as in A000009.

%C Without the restriction that the parts be distinct, the terms a(n) would be infinite: e.g. 5 = 5 + any number of copies of (1+2+3+4).

%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>

%e a(6) = 7: 6 = 6+5+4+1 = 6+5+3+2 = 6+4+3+2+1 = 5+1 = 4+2 = 3+2+1.

%e a(7) = 13: 7 = 6+1 = 5+2 = 4+3 = 4+2+1 = 7+6+4 = 7+6+3+1 = 7+5+4+1 = 7+5+3+2 = 7+4+3+2+1 = 6+5+4+2 = 6+5+3+2+1 = 7+6+5+4+3+2.

%Y Cf. A000009.

%K nonn,base

%O 0,4

%A _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Jul 20 2010

%E Missing initial a(0)=1 value inserted by _Marc LeBrun_, Oct 26 2010