A126944 - OEIS

%I #18 Mar 07 2024 16:36:53

%S 1,5,15,47,149,469,1477,4657,14677,46251,145765,459391,1447783,

%T 4562753,14379751,45318455,142823219,450114149,1418555997,4470646047,

%U 14089451907,44403572399,139939952691,441027361411,1389918532165,4380393813543,13805017716305

%N The sequence a[n]+b[n]+c[n]+d[n] defined in A126939.

%C Linear recurrence and empirical g.f confirmed for more terms. - _Ray Chandler_, Mar 07 2024

%H Ray Chandler, <a href="/A126944/b126944.txt">Table of n, a(n) for n = 0..2005</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, 7, 3, 3, 1).

%F Empirical g.f.: -(x^5 +2*x^4 +5*x^3 +4*x^2 +3*x +1) / (x^6 +3*x^5 +3*x^4 +7*x^3 +x^2 +2*x-1). - _Colin Barker_, Apr 08 2013

%t a[0] = 1; a[1] = 5; a[2] = 15; a[3] = 47; a[4] = 149; a[5] = 469; a[n_] := a[n] = a[n-6] + 3*a[n-5] + 3*a[n-4] + 7*a[n-3] + a[n-2] + 2*a[n-1]; Table[a[n], {n, 0, 26}] (* _Jean-François Alcover_, Nov 23 2016 *)

%t LinearRecurrence[{2, 1, 7, 3, 3, 1}, {1, 5, 15, 47, 149, 469}, 27] (* or *)

%t CoefficientList[ Series[-(x^5 + 2x^4 + 5x^3 + 4x^2 + 3x + 1)/(x^6 + 3x^5 + 3x^4 + 7x^3 + x^2 + 2x -1), {x, 0, 26}], x] (* _Robert G. Wilson v_, Nov 23 2016 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 18 2007