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A055988 Sequence is its own 4th difference.

%I A055988 #29 Jul 02 2025 16:02:00
%S A055988 1,2,7,26,95,345,1252,4544,16493,59864,217286,788674,2862617,10390321,
%T A055988 37713313,136886433,496850954,1803399103,6545722210,23758733815,
%U A055988 86236081273,313007493212,1136110191472,4123691589365,14967590689568
%N A055988 Sequence is its own 4th difference.
%C A055988 Row sums of Riordan array (1/(1-x), x/(1-x)^4), A109960. - _Paul Barry_, Jul 06 2005
%H A055988 Vincenzo Librandi, <a href="/A055988/b055988.txt">Table of n, a(n) for n = 1..1000</a>
%H A055988 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,4,-1).
%F A055988 a(n) = 5a(n-1) - 6a(n-2) + 4a(n-3) - a(n-4) = a(n-1) + A055991(n-1) = A055989(n) - A055989(n-1) = A055990(n) - 2*A055990(n-1) + A055990(n-2).
%F A055988 From _Paul Barry_, Jul 06 2005: (Start)
%F A055988 G.f.: (1-x)^3/(1 - 5x + 6x^2 - 4x^3 + x^4);
%F A055988 a(n) = Sum_{k=0..n} binomial(n+3k, 4k). (End)
%t A055988 CoefficientList[Series[(1-x)^3/(1-5x+6x^2-4x^3+x^4),{x,0,40}],x] (* _Vincenzo Librandi_, Apr 05 2012 *)
%t A055988 LinearRecurrence[{5,-6,4,-1},{1,2,7,26},30] (* _Harvey P. Dale_, Jan 15 2017 *)
%o A055988 (Magma) I:=[1, 2, 7, 26]; [n le 4 select I[n] else 5*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 05 2012
%Y A055988 Cf. A055989, A055990, A055991 for the other differences of a(n). See A000079, A001906, A052529 for examples of sequences which are respectively their own first, second and third differences.
%K A055988 nonn,easy
%O A055988 1,2
%A A055988 _Henry Bottomley_, Jun 02 2000
%E A055988 More terms from _James Sellers_, Jun 05 2000