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a(n) = 81*n - 59.
1

%I #27 Sep 08 2022 08:45:41

%S 22,103,184,265,346,427,508,589,670,751,832,913,994,1075,1156,1237,

%T 1318,1399,1480,1561,1642,1723,1804,1885,1966,2047,2128,2209,2290,

%U 2371,2452,2533,2614,2695,2776,2857,2938,3019,3100,3181,3262,3343,3424,3505,3586

%N a(n) = 81*n - 59.

%H Vincenzo Librandi, <a href="/A156795/b156795.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1) - a(n-2).

%F G.f.: x*(22 + 59*x)/(1-x)^2.

%F E.g.f.: 59 - (59 - 81*x)*exp(x). - _G. C. Greubel_, Jun 26 2021

%t LinearRecurrence[{2,-1},{22,103},50]

%t 81*Range[50]-59 (* _Harvey P. Dale_, Jun 01 2020 *)

%o (Magma) I:=[22, 103]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n)=81*n-59 \\ _Charles R Greathouse IV_, Dec 23 2011

%o (Sage) [81*n - 59 for n in (1..50)] # _G. C. Greubel_, Jun 26 2021

%Y Cf. A156796, A156797.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 16 2009