A036549 - OEIS

%I #18 Aug 29 2024 22:39:15

%S 1,257,1025,3329,10241,30977,93185,279809,839681,2519297,7558145,

%T 22674689,68024321,204073217,612219905,1836659969,5509980161,

%U 16529940737,49589822465,148769467649,446308403201,1338925209857,4016775629825,12050326889729,36150980669441

%N a(n) = T(8,n), array T given by A048471.

%C n-th difference of a(n), a(n-1), ..., a(0) is 2^(n+7) for n=1, 2, 3, ...

%H Vincenzo Librandi, <a href="/A036549/b036549.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F From _Vincenzo Librandi_, Nov 11 2011: (Start)

%F a(n) = 128*3^n - 127.

%F a(n) = 3*a(n-1) + 254.

%F a(n) = 4*a(n-1) - 3*a(n-2).

%F G.f.: (1+253*x)/((1-x)*(1-3*x)). (End)

%F E.g.f.: exp(x)*(128*exp(2*x) - 127). - _Elmo R. Oliveira_, Aug 29 2024

%o (Magma) [128*3^n-127: n in [0..30]]; // _Vincenzo Librandi_, Nov 11 2011

%Y Cf. A048471.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_