|
%I #24 Sep 08 2022 08:44:37
%S 2,5,16,52,152,392,904,1899,3694,6743,11672,19318,30772,47426,71024,
%T 103717,148122,207385,285248,386120,515152,678316,882488,1135535,
%U 1446406,1825227,2283400,2833706,3490412,4269382,5188192,6266249
%N M-sequences m_0,m_1,m_2,m_3 with m_1 < n.
%D S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
%H Vincenzo Librandi, <a href="/A011819/b011819.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n)= ( 2*n^6 +15*n^5 +50*n^4 +165*n^3 +308*n^2 +540*n +720 )/360. [_Frank Ellermann_]
%F G.f.: -x*(x^6-7*x^5+19*x^4-25*x^3+23*x^2-9*x+2) / (x-1)^7. - _Colin Barker_, Feb 15 2014
%t CoefficientList[Series[(x^6 - 7 x^5 + 19 x^4 -25 x^3 + 23 x^2 - 9 x + 2)/(1 - x)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 16 2014 *)
%o (PARI) a(n)=n*(2*n^5+15*n^4+50*n^3+165*n^2+308*n+540)/360+2 \\ _Charles R Greathouse IV_, Dec 08 2011
%o (PARI) Vec(-x*(x^6-7*x^5+19*x^4-25*x^3+23*x^2-9*x+2)/(x-1)^7 + O(x^100)) \\ _Colin Barker_, Feb 15 2014
%o (Magma) [n*(2*n^5+15*n^4+50*n^3+165*n^2+308*n+540)/360+2: n in [0..40]]; // _Vincenzo Librandi_, Feb 16 2014
%Y Cf. A011820-A011825, A011827.
%K nonn,easy
%O 1,1
%A Svante Linusson (linusson(AT)math.kth.se)
|
