Search: id:A071976
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%I A071976
%S A071976 1,2,6,20,70,252,924,3432,12870,48619,184735,705222,2702609,10390940,
%T A071976 40062132,154830696,599641425,2326640877,9042327525,35194002709,
%U A071976 137160956815,535193552973,2090558951396,8174176541450,31990402045260
%N A071976 Lists of length n from {0..9} summing to n but not beginning with 0.
%C A071976 Number of n-digit numbers with digit sum n.
%F A071976 Equals binomial(2n-2, n-1) for n <= 9, by the stars and bars argument. 
               [To get such a number take n boxes in which the left-most box contains 
               a 1 and the rest are empty. Distribute the remaining n-1 1's into 
               the n boxes subject to the constraint that no box contains more than 
               9 1's. This can be done in binomial(2n-2, n-1) ways for n <= 9.]
%e A071976 a(3) = 6 as there are six three-digit numbers with digit sum 3: 102, 
               111, 120, 201, 210, 300.
%e A071976 a(10) = binomial(18,9)-1; a(11) = binomial(20,10)-21; a(12) = binomial(22,
               11)-210.
%t A071976 Do[c = 0; k = 10^n; l = 10^(n + 1) - 1; While[k < l, If[ Plus @@ IntegerDigits[k] 
               == n + 1, c++ ]; k++ ]; Print[c], {n, 0, 7}]
%o A071976 (PARI) a(n)=local(y=(x^10-1)/(x-1)); if(n<1,0,polcoeff((y-1)*y^(n-1),
               n))
%Y A071976 Different from A000984.
%Y A071976 Sequence in context: A087944 A056616 A065346 this_sequence A000984 A087433 
               A119373
%Y A071976 Adjacent sequences: A071973 A071974 A071975 this_sequence A071977 A071978 
               A071979
%K A071976 nonn,base
%O A071976 1,2
%A A071976 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2002
%E A071976 Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Jun 20, 2002.
%E A071976 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 21 2002
%E A071976 More terms from John W. Layman (layman(AT)math.vt.edu), Jun 22 2002

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