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Sequence equals its 4th differences shifted by one index.
1

%I #22 Apr 10 2024 10:32:52

%S 1,3,7,15,32,70,156,349,778,1728,3833,8505,18884,41943,93160,206897,

%T 459459,1020311,2265815,5031792,11174374,24815508,55108933,122382762,

%U 271780616,603555049,1340341377,2976555532,6610168495,14679492624

%N Sequence equals its 4th differences shifted by one index.

%C Binomial transform yields A079398 without the initial (0,1,1,1). - _R. J. Mathar_, Apr 09 2008

%H Vincenzo Librandi, <a href="/A137166/b137166.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-1).

%F a(n) = 4*a(n-1)-6*a(n-2)+5*a(n-3)-a(n-4). - _R. J. Mathar_, Apr 09 2008

%F G.f.: (x^2 - x + 1) / (x^4 - 5*x^3 + 6*x^2 - 4*x + 1). - _Alexander R. Povolotsky_, Apr 08 2008

%t s = ""; a = 0; b = 1; c = 1; d = 1; For[i = 0, i < 23, a = a + b; s = s <> ToString[a] <> ","; b = b + c; c = c + d; d = d + a; i++ ]; Print[s]

%t LinearRecurrence[{4, -6, 5, -1}, {1, 3, 7, 15}, 40] (* _Vincenzo Librandi_, Jun 15 2013 *)

%o (Magma) [n le 4 select 2^n-1 else 4*Self(n-1)-6*Self(n-2)+5*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jun 15 2013

%o (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -1,5,-6,4]^n*[1;3;7;15])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Cf. A079398.

%K nonn,easy

%O 0,2

%A _Vladimir Joseph Stephan Orlovsky_, Apr 03 2008

%E Edited by _R. J. Mathar_, Apr 09 2008

%E Edited by _Bruno Berselli_, Apr 07 2011