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A099671 Partial sums of repdigits of A002278. 0

%I #12 Jul 02 2023 18:59:24

%S 4,48,492,4936,49380,493824,4938268,49382712,493827156,4938271600,

%T 49382716044,493827160488,4938271604932,49382716049376,

%U 493827160493820,4938271604938264,49382716049382708,493827160493827152

%N Partial sums of repdigits of A002278.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12, -21, 10).

%F a(n) = (4/81)*(10^(n+1) - 9*n - 10). - R. Piyo (nagoya314(AT)yahoo.com), Dec 10 2004

%F From _Chai Wah Wu_, Feb 28 2018: (Start)

%F a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 3.

%F G.f.: 4*x/((1 - x)^2*(1 - 10*x)). (End)

%e 4 + 44 + 444 + 4444 + 44444 = a(5) = 49380.

%t <<NumberTheory`NumberTheoryFunctions` Table[{k, Table[Apply[Plus, Table[k*(10^n-1)/9, {n, 1, m}]], {m, 1, 35}]}, {k, 1, 9}]

%t Table[4/9*Sum[10^i - 1, {i, n}], {n, 18}] (* _Robert G. Wilson v_, Nov 20 2004 *)

%Y Cf. A057932, A002275-A002283.

%K base,nonn

%O 1,1

%A _Labos Elemer_, Nov 17 2004

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)