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%I #16 Mar 06 2017 19:49:01
%S 1,7,28,84,210,462,924,1716,3003,5004,7995,12306,18312,26418,37038,
%T 50568,67353,87648,111573,139068,169863,203463,239148,275988,312873,
%U 348558,381723,411048,435303,453438,464653,468448,464653,453438,435303,411048,381723,348558,312873,275988,239148,203463,169863,139068,111573,87648,67353,50568,37038,26418,18312,12306,7995,5004,3003,1716,924,462,210,84,28,7,1
%N Number of 7-digit numbers whose sum of digits is n.
%C There are 9000000 numbers with 7 decimal digits, the smallest being 1000000 and the largest 9999999.
%C Differs for n >= 10 (5004 vs 5005) from A000579(n+5) = binomial(n+5,6). - _M. F. Hasler_, Mar 05 2017
%F G.f.: (x - x^10)/(1 - x)*((1 - x^10)/(1 - x))^6. - _Michael De Vlieger_, Dec 07 2016
%F a(64-n) = a(n), 1 <= n <= 63. - _M. F. Hasler_, Mar 05 2017
%e a(2)=7: 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 2000000.
%t Rest@ CoefficientList[Series[(x - x^10)/(1 - x) ((1 - x^10)/(1 - x))^#, {x, 0, 9 (# + 1)}], x] &@ 6 (* or *)
%t Function[w, Count[w, #] & /@ Range[Max@ w]]@ Map[Total@ IntegerDigits@ # &, Range[10^#, 10^(# + 1) - 1]] &@ 6 (* _Michael De Vlieger_, Dec 07 2016 *)
%o (PARI) b=vector(63, i, 0); for(n=1000000, 9999999, a=eval(Vec(Str(n))); b[sum(j=1, 7, a[j])]++); for(n=1, 63, print1(b[n], ", "))
%o (PARI) Vec((1-x^9)*(1-x^10)^6/(1-x)^7) \\ shorter than (1-x^9)/(1-x)*((1-x^10)/(1-x))^6, but not better. - _M. F. Hasler_, Mar 05 2017
%Y A071817 (3-digit numbers), A090579 (4-digit numbers), A090580 (5-digit numbers), A090581 (6-digit numbers), A278971 (8-digit numbers).
%K base,fini,full,nonn,easy
%O 1,2
%A _Daniel Mondot_, Dec 02 2016