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A272525 Convolution of nonzero repunits (A002275) with themselves.

%I A272525 #24 Feb 16 2025 08:33:34
%S A272525 1,22,343,4664,58985,713306,8367627,96021948,1083676269,12071330590,
%T A272525 133058984911,1454046639232,15775034293553,170096021947874,
%U A272525 1824417009602195,19478737997256516,207133058984910837,2194787379972565158,23182441700960219479,244170096021947873800
%N A272525 Convolution of nonzero repunits (A002275) with themselves.
%C A272525 Partial sums of A014925.
%H A272525 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%H A272525 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-141,220,-100)
%F A272525 O.g.f.: 1/((1 - 10*x)^2*(1 - x)^2).
%F A272525 E.g.f.: (29 + 9*x  + 700*exp(9*x) + 9000*x*exp(9*x))*exp(x)/729.
%F A272525 a(n) =  22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4).
%F A272525 a(n) = (9*n(10^(n+2) + 1) + 7*10^(n+2) + 29)/729.
%F A272525 A010879(a(n)) = A010879(n+1).
%t A272525 LinearRecurrence[{22, -141, 220, -100}, {1, 22, 343, 4664}, 20]
%t A272525 Table[(9 n (10^(n + 2) + 1) + 7 10^(n + 2) + 29)/729, {n, 0, 19}]
%o A272525 (PARI) A272525(n)=(9*n+7)*(10^(n+2)+1)\729+1 \\ _M. F. Hasler_, Nov 02 2016
%Y A272525 Cf. A002275, A010879, A014925, A083449.
%K A272525 base,nonn,easy
%O A272525 0,2
%A A272525 _Ilya Gutkovskiy_, May 02 2016