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%I #14 Sep 10 2021 02:07:35
%S 0,26,1326,50726,1725126,55009526,1684153926,50135658326,
%T 1462218522726,41984966747126,1190791264331526,33440126095275926,
%U 931432109043580326,25766955599293244726,708683864685628269126,19394355959426432653526,528467641885089690397926
%N Number of words with n letters from an alphabet of size 26 with at least two equal consecutive letters.
%H Colin Barker, <a href="/A106710/b106710.txt">Table of n, a(n) for n = 1..706</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (51,-650).
%F a(n) = 26^n - 26*25^(n - 1).
%F From _Colin Barker_, Nov 05 2015: (Start)
%F a(n) = 51*a(n-1) - 650*a(n-2) for n>2.
%F G.f.: 26*x^2 / ((1-25*x)*(1-26*x)). (End)
%F From _G. C. Greubel_, Sep 10 2021: (Start)
%F a(n) = 26*(A009970(n-1) - A009969(n-1)).
%F E.g.f.: exp(26*x) - (26/25)*exp(25*x). (End)
%e a(3) = 1326 because 26^3 - 26*(25^2) = 1326.
%t Table[26*(26^(n-1) -25^(n-1)), {n, 25}] (* _G. C. Greubel_, Sep 10 2021 *)
%o (PARI) a(n) = 26^n - 26*(25^(n - 1)); \\ _Michel Marcus_, Aug 14 2013
%o (PARI) concat(0, Vec(26*x^2/((25*x-1)*(26*x-1)) + O(x^100))) \\ _Colin Barker_, Nov 05 2015
%o (Sage) [26*(26^(n-1) - 25^(n-1)) for n in (1..25)] # _G. C. Greubel_, Sep 10 2021
%Y Cf. A009969, A009970,
%K nonn,easy
%O 1,2
%A _Luca Colucci_, May 14 2005
%E More terms from _Michel Marcus_, Aug 14 2013
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