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 A081586 Fourth row of Pascal-(1,3,1) array A081578. 3

%I

%S 1,13,73,245,593,1181,2073,3333,5025,7213,9961,13333,17393,22205,

%T 27833,34341,41793,50253,59785,70453,82321,95453,109913,125765,143073,

%U 161901,182313,204373,228145,253693,281081,310373,341633,374925,410313,447861

%N Fourth row of Pascal-(1,3,1) array A081578.

%H Vincenzo Librandi, <a href="/A081586/b081586.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F From _Harvey P. Dale_, Nov 06 2011: (Start)

%F a(n) = (3 + 28*n - 24*n^2 + 32*n^3)/3.

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

%F a(0)=1, a(1)=13, a(2)=73, a(3)=245, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

%F E.g.f.: (1/3)*(3 + 36*x + 72*x^2 + 32*x^3)*exp(x). - _G. C. Greubel_, May 26 2021

%t Table[(3+28n-24n^2+32n^3)/3,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,13,73,245},40] (* _Harvey P. Dale_, Nov 06 2011 *)

%o (MAGMA) [(3+28*n-24*n^2+32*n^3)/3: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2011

%o (Sage) [(3+28*n-24*n^2+32*n^3)/3 for n in (0..40)] # _G. C. Greubel_, May 26 2021

%Y Cf. A081578, A081585.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 23 2003

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Last modified July 28 23:07 EDT 2021. Contains 346340 sequences. (Running on oeis4.)