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%I #9 Sep 23 2023 03:11:02
%S 1,1,4,2,1,11,9,15,256,0,0,408,307,387,511,1608,3821,43207,13651,0,
%T 147897,115063,179695,938500,133868,844163,21955502,3756136,9067127,0,
%U 33861703,46269686,177316890,163959413,75053719,6678119984,1776064204
%N Number of multiples of n with no zero digit with sum of digits = n.
%e a(3) = 4, the multiples being 3, 12, 21, 111. a(4) = 2 the partition of 4 are (4), (3, 1), (2, 2), (2, 1, 1), (1, 1, 1, 1).and the two multiples of 4 obtained by rearranging the digits are 4 and 112.
%e a(6) = 11: 6*1=6,6*4=24,6*7=42,6*19=114,6*22=132,6*37=222,6*52=312,6*187=1122,6*202=1212,6*352=2112,6*1852=11112
%e a(7) = 9: 7*1=7,7*19=133,7*46=322,7*73=511,7*163=1141,7*316=2212,7*1603=11221,7*1873=13111,7*3016=21112
%e a(8) = 15: 8*1=8,8*19=152,8*28=224,8*64=512,8*154=1232,8*289=2312,8*514=4112,8*1414=11312,8*1639=13112,8*2764=22112,8*3889=31112,8*14014=112112,8*15139=121112,8*26389=211112,8*138889=1111112
%o (PARI) a(n) = local (pv, c, T, newT, x); pv = 1; c = 0; T = matrix(n, n); for (i = 1, min(n, 9), T[1 + n - i, 1 + i%n] = 1); for (k = 1, n - 1, pv = pv*10%n; newT = matrix(n - k, n); for (j = 1, n, newT[1, j] = T[1, j]); for (i = 2, n - k + 1, for (j = 1, n, x = T[i, j]; if (x, for (d = 1, min (i - 1, 9), newT[i - d, (j - 1 + d*pv)%n + 1] += x)))); T = newT); T[1, 1]; \\ _David Wasserman_, Jan 18 2005
%Y Number of terms in the n-th row of A077755.
%K base,nonn
%O 1,3
%A _Amarnath Murthy_, Sep 23 2002
%E a(6)-a(10) from Deepan Majmudar (deepan.majmudar(AT)hp.com), Dec 03 2004
%E More terms from _David Wasserman_, Jan 18 2005
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