A294433 Expansion of (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^5.
1, 16, 94, 331, 871, 1906, 3676, 6469, 10621, 16516, 24586, 35311, 49219, 66886, 88936, 116041, 148921, 188344, 235126, 290131, 354271, 428506, 513844, 611341, 722101, 847276, 988066, 1145719, 1321531, 1516846, 1733056, 1971601, 2233969, 2521696, 2836366
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
- J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702. See Table 2.
- J. A. De Loera, D. C. Haws and M. Koppe, Ehrhart Polynomials of Matroid Polytopes and Polymatroids, arXiv:0710.4346 [math.CO], 2007; Discrete Comput. Geom., 42 (2009), 670-702.
- D. C. Haws, Matroids [Broken link, Oct 30 2017]
- D. C. Haws, Matroids [Copy on website of Matthias Koeppe]
- D. C. Haws, Matroids [Cached copy, pdf file only]
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4: n in [0..30]]; // G. C. Greubel, Apr 29 2018
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Maple
seq(1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4,n=0..30); # Robert Israel, Oct 30 2017
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Mathematica
Table[1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4, {n, 0, 30}] (* or *) LinearRecurrence[{5,-10,10,-5,1}, {1, 16, 94, 331, 871}, 30] (* G. C. Greubel, Apr 29 2018 *) -
PARI
Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Oct 31 2017
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PARI
a(n) = my(t=n*(n+1)/2); 8*t^2+7*t+1; \\ Altug Alkan, Apr 30 2018
Formula
a(n) = 1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4. - Robert Israel, Oct 30 2017
From Colin Barker, Oct 31 2017: (Start)
G.f.: (1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4.
(End)