A160791 a(n) = binomial(N, n - N) where N = 1 + floor(n/2).
0, 1, 1, 2, 3, 3, 6, 4, 10, 5, 15, 6, 21, 7, 28, 8, 36, 9, 45, 10, 55, 11, 66, 12, 78, 13, 91, 14, 105, 15, 120, 16, 136, 17, 153, 18, 171, 19, 190, 20, 210, 21, 231, 22, 253, 23, 276, 24, 300, 25, 325, 26, 351, 27, 378, 28, 406, 29, 435, 30, 465
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
Programs
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Magma
[(n^2+6*n+4+(n^2-2*n-4)*(-1)^n)/16: n in [0..70]]; // Vincenzo Librandi, Apr 02 2015
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Maple
a := proc(n) 1 + floor(n/2); binomial(%, n - %) end: seq(a(n), n = 0..60); # Peter Luschny, Jul 02 2024
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Mathematica
Join[{0}, Riffle[Range[30], Range[30] (Range[30] + 1)/2]] (* Bruno Berselli, Jul 15 2013 *) LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 1, 2, 3, 3, 6}, 60] (* Vincenzo Librandi, Apr 02 2015 *) -
PARI
Vec(x*(1+x-x^2)/(1-x^2)^3 + O(x^80)) \\ Michel Marcus, Apr 01 2015
Formula
From R. J. Mathar, Feb 09 2010: (Start)
a(2n+1) = n+1 and a(2n) = A000217(n) with a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
G.f.: x*(1+x-x^2)/(1-x^2)^3. (End)
a(n) = (n^2+6*n+4+(n^2-2*n-4)*(-1)^n)/16. - Luce ETIENNE, Mar 31 2015
E.g.f.: (x*(x+4)*cosh(x) + (3*x+4)*sinh(x))/8. - G. C. Greubel, Apr 26 2018
Extensions
a(0) = 0 prepended and new name by Peter Luschny, Jul 02 2024
Comments