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A210677 a(n) = a(n-1) + a(n-2) + n + 1, a(0) = a(1) = 1. 2

%I #33 Feb 24 2023 07:01:58

%S 1,1,5,10,20,36,63,107,179,296,486,794,1293,2101,3409,5526,8952,14496,

%T 23467,37983,61471,99476,160970,260470,421465,681961,1103453,1785442,

%U 2888924,4674396,7563351,12237779,19801163,32038976,51840174,83879186,135719397,219598621,355318057

%N a(n) = a(n-1) + a(n-2) + n + 1, a(0) = a(1) = 1.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-1,1).

%F From _Colin Barker_, Jun 30 2012: (Start)

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

%F G.f.: (1 - 2*x + 4*x^2 - 2*x^3)/((1 - x)^2*(1 - x - x^2)). (End)

%F E.g.f.: exp(x/2)*(25*cosh(sqrt(5)*x/2) + 7*sqrt(5)*sinh(sqrt(5)*x/2))/5 - exp(x)*(4 + x). - _Stefano Spezia_, Feb 24 2023

%t LinearRecurrence[{3, -2, -1, 1}, {1, 1, 5, 10}, 39] (* _Jean-François Alcover_, Oct 05 2017 *)

%Y Cf. A081659: a(n)=a(n-1)+a(n-2)+n-5, a(0)=a(1)=1 (except first 2 terms and sign).

%Y Cf. A001924: a(n)=a(n-1)+a(n-2)+n-4, a(0)=a(1)=1 (except first 4 terms).

%Y Cf. A000126: a(n)=a(n-1)+a(n-2)+n-2, a(0)=a(1)=1 (except first term).

%Y Cf. A066982: a(n)=a(n-1)+a(n-2)+n-1, a(0)=a(1)=1.

%Y Cf. A030119: a(n)=a(n-1)+a(n-2)+n, a(0)=a(1)=1.

%Y Cf. A210678: a(n)=a(n-1)+a(n-2)+n+2, a(0)=a(1)=1.

%K nonn,easy

%O 0,3

%A _Alex Ratushnyak_, May 09 2012

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)