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A178510 a(n+1) = a(n)*100 + 21^n, with a(1)=1.

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%I A178510 #33 Apr 08 2024 12:31:43
%S A178510 1,121,12541,1263361,126530581,12657142201,1265799986221,
%T A178510 126581799710641,12658217793923461,1265822573672392681,
%U A178510 126582274047120246301,12658227754989525172321,1265822782854780028618741,126582278439950380600993561,12658227847238957992620864781
%N A178510 a(n+1) = a(n)*100 + 21^n, with a(1)=1.
%C A178510 Related to decimal expansion of fraction 1/79 and Pell numbers.
%H A178510 Vincenzo Librandi, <a href="/A178510/b178510.txt">Table of n, a(n) for n = 1..200</a>
%H A178510 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (121,-2100).
%F A178510 a(n) = 121*a(n-1) - 2100*a(n-2). - _Harvey P. Dale_, Sep 09 2011
%F A178510 G.f.: x/(1 - 121*x + 2100*x^2). - _Philippe Deléham_, Oct 11 2011
%t A178510 Rest[RecurrenceTable[{a[0]==0,a[n]==100a[n-1]+21^(n-1)},a[n],{n,15}]] (* or *) LinearRecurrence[{121,-2100},{1,121},20] (* _Harvey P. Dale_, Sep 09 2011 *)
%o A178510 (Magma) [(1/79)*(100^n-21^n): n in [1..20]]; // _Vincenzo Librandi_, Sep 13 2011
%o A178510 (PARI) a(n)=(100^n-21^n)/79 \\ _Charles R Greathouse IV_, Oct 10 2011
%Y A178510 Cf. A000129, A021083, A038207.
%K A178510 nonn,easy
%O A178510 1,2
%A A178510 _Mark Dols_, May 29 2010
%E A178510 Removed vacuous a(0)=0 from NAME. - _R. J. Mathar_, Jun 19 2021