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 A294433 Expansion of (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^5. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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/a> [Cached copy, pdf file only] Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). 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) MAPLE seq(1 + 7*n/2 + 11*n^2/2 + 4*n^3 + 2*n^4, n=0..30); # Robert Israel, Oct 30 2017 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 *) PROG (PARI) Vec((1 + 11*x + 24*x^2 + 11*x^3 + x^4) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Oct 31 2017 (PARI) a(n) = my(t=n*(n+1)/2); 8*t^2+7*t+1; \\ Altug Alkan, Apr 30 2018 (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 CROSSREFS Sequence in context: A316215 A305639 A317033 * A160750 A305908 A316880 Adjacent sequences: A294430 A294431 A294432 * A294434 A294435 A294436 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Oct 30 2017 STATUS approved

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Last modified June 4 19:24 EDT 2023. Contains 363128 sequences. (Running on oeis4.)