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A328352 Similar to A328350, but for 5 digits rather then 3. 8

%I

%S 0,1,56,2831,141706,7086081,354307956,17715417331,885770964206,

%T 44288548698581,2214427437370456,110721371880729831,

%U 5536068594097526706,276803429705181511081,13840171485260601432956,692008574263037701042331,34600428713151923199089206,1730021435657596350689323581

%N Similar to A328350, but for 5 digits rather then 3.

%C This sequence is the building block for the calculation of the sums of positive integers whose decimal expansion only uses five distinct, nonzero digits: see the attached pdf document.

%H Pierre-Alain Sallard, <a href="/A328352/b328352.txt">Table of n, a(n) for n = 0..50</a>

%H Pierre-Alain Sallard, <a href="/A328352/a328352.pdf">Integers sequences A328348 and A328350 to A328356</a>

%F a(n) = (40*50^n - 49*5^n + 9) / 1764.

%F a(n) = 51*a(n-1) - 50*a(n-2) + 5^(n-1) for n > 1.

%F G.f.: x / (1 - 56*x + 305*x^2 - 250*x^3).

%F a(n) = 56*a(n-1) - 305*a(n-2) + 250*a(n-3) for n > 2.

%e For n=2, the sum of all positive integers whose decimal notation is only made of the 3,4,5,6 and 7 digit with at most n=2 such digits, i.e. the sum 3+4+5+6+7+33+34+35+36+37+43+44+45+46+47+53+54+55+56+57+63+64+65+66+67+73+74+75+76+77 is equal to a(2)*(3+4+5+6+7) = 56*25 = 1400.

%e The formula is valid for any other 5-tuple of digits, as soon as the 5 digits are different from each other. Always with n=2 but let's say with the 5,6,7,8 and 9 digits, the sum 5+6+7+8+9+55+56+57+58+59+65+66+67+68+69+75+76+77+78+79+85+86+87+88+89+95+96+97+98+99 is equal to a(2)*(5+6+7+8+9) = 56*35 = 1960.

%o (Python) [(40*50**n-49*5**n+9)//1764 for n in range(12)]

%Y Cf. A328348, A328350, A328351, A328353, A328354, A328355, A328356.

%K nonn,base

%O 0,3

%A _Pierre-Alain Sallard_, Nov 26 2019

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Last modified October 23 11:52 EDT 2021. Contains 348212 sequences. (Running on oeis4.)