A011819 M-sequences m_0,m_1,m_2,m_3 with m_1 < n.

2, 5, 16, 52, 152, 392, 904, 1899, 3694, 6743, 11672, 19318, 30772, 47426, 71024, 103717, 148122, 207385, 285248, 386120, 515152, 678316, 882488, 1135535, 1446406, 1825227, 2283400, 2833706, 3490412, 4269382, 5188192, 6266249

Offset: 1

Author

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

Keywords

• nonn
• easy

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A011820-A011825, A011827.

Programs

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

Mathematica

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 *)

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

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

Formula

a(n)= ( 2*n^6 +15*n^5 +50*n^4 +165*n^3 +308*n^2 +540*n +720 )/360. [Frank Ellermann]

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