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%I #16 Feb 08 2022 22:26:39
%S 1,4,11,33,79,158,279,451,683,984,1363,1829,2391,3058,3839,4743,5779,
%T 6956,8283,9769,11423,13254,15271,17483,19899,22528,25379,28461,31783,
%U 35354,39183,43279,47651,52308,57259,62513,68079,73966
%N (1, 4, 7, 10, 13, ...) convolved with (1, 0, 4, 7, 10, 13, ...); given A016777 = (1, 4, 7, 10, 13, ...).
%H Vincenzo Librandi, <a href="/A179905/b179905.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,-6,4,-1).
%F (1 + 4x + 11x^2 + 33x^3 + ...) = (1 + 4x + 10x^2 + 13x^3 + ...) *
%F (1 + 4x^2 + 10x^3 + 13x^4 + ...).
%F G.f. 1 -x*(x-4)*(3*x^2-x+1)/(x-1)^4. - _R. J. Mathar_, Apr 04 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jul 04 2012
%e a(4) = 79 = (13, 10, 7, 4, 1) dot (1, 0, 4, 7, 10) = (13 + 0 + 28 + 28 + 10).
%t CoefficientList[Series[1-x*(x-4)*(3*x^2-x+1)/(x-1)^4,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 04 2012 *)
%t Join[{1},LinearRecurrence[{4,-6,4,-1},{4,11,33,79},40]] (* _Harvey P. Dale_, Jun 24 2014 *)
%o (Magma) I:=[1, 4, 11, 33, 79]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jul 04 2012
%Y Cf. A016777.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Jul 31 2010
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