%I #17 Jul 23 2024 19:43:31

%S 1,13,121,997,7729,57853,423721,3059797,21887329,155555053,1100604121,

%T 7762822597,54632726929,383893932253,2694581744521,18898693305397,

%U 132473958606529,928233237589453,6502210299844921,45538360282508197,318882962895526129,2232752944858526653

%N 6th binomial transform of the periodic sequence (1,7,1,1,7,1...).

%H Vincenzo Librandi, <a href="/A081033/b081033.txt">Table of n, a(n) for n = 0..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35).

%F a(n) = 7*a(n-1) + 6*5^(n-1).

%F a(n) = 4*7^n - 3*5^n.

%F G.f.: (1+x)/((1-5*x)*(1-7*x)). - _Vincenzo Librandi_, Aug 06 2013

%F E.g.f.: exp(5*x)*(4*exp(2*x) - 3). - _Stefano Spezia_, Jul 23 2024

%t CoefficientList[Series[(1 + x) / ((1 - 5 x) (1 - 7 x)),{x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)

%t LinearRecurrence[{12,-35},{1,13},30] (* _Harvey P. Dale_, Aug 18 2015 *)

%o (Magma) [4*7^n-3*5^n: n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013

%Y Cf. A080134, A080962.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Mar 03 2003