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Number of M-sequences m_0,...,m_5 with m_1 < n.
1

%I #23 Nov 24 2019 13:16:32

%S 2,7,64,877,10742,102050,753994,4486435,22285884,95264798,359074648,

%T 1216716022,3763991016,10763615106,28741372964,72261453121,

%U 172248589406,391536067037,852876877928,1787799809335,3619382778994

%N Number of M-sequences m_0,...,m_5 with m_1 < n.

%C Apparently a polynomial of degree 15: n^15/32659200 etc., compare A011829. [_Frank Ellermann_]

%D S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.

%H Vincenzo Librandi, <a href="/A011821/b011821.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

%F G.f.: -x*(x^15 -16*x^14 +118*x^13 -532*x^12 +1648*x^11 -3712*x^10 +5776*x^9 -12080*x^8 -2775*x^7 -21034*x^6 -3582*x^5 -4110*x^4 +427*x^3 -192*x^2 +25*x -2)/(x -1)^16. [_Colin Barker_, Sep 18 2012]

%t CoefficientList[Series[- (x^15 - 16 x^14 + 118 x^13 - 532 x^12 + 1648 x^11 - 3712 x^10 + 5776 x^9 - 12080 x^8 - 2775 x^7 - 21034 x^6 - 3582 x^5 - 4110 x^4 + 427 x^3 - 192 x^2 + 25 x - 2)/(x - 1)^16, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)

%t LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{2,7,64,877,10742,102050,753994,4486435,22285884,95264798,359074648,1216716022,3763991016,10763615106,28741372964,72261453121},30] (* _Harvey P. Dale_, Nov 24 2019 *)

%Y Cf. A011819-A011825, A011829.

%K nonn,easy

%O 1,1

%A Svante Linusson (linusson(AT)math.kth.se)