A199935
Size (b^3_n) of unit sphere in a certain graph (see Hazama article for precise definition).
Original entry on oeis.org
0, 0, 2, 5, 9, 14, 22, 36, 60, 99, 161, 260, 420, 680, 1102, 1785, 2889, 4674, 7562, 12236, 19800, 32039, 51841, 83880, 135720, 219600, 355322, 574925, 930249, 1505174, 2435422, 3940596, 6376020, 10316619, 16692641, 27009260, 43701900, 70711160, 114413062, 185124225
Offset: 2
- Vincenzo Librandi, Table of n, a(n) for n = 2..1000
- Fumio Hazama, Spectra of graphs attached to the space of melodies, Discr. Math., 311 (2011), 2368-2383. See Table 2.1.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-1).
-
CoefficientList[Series[-x^2*(-2+x)/((x-1)*(x^2-x+1)*(x^2+x-1)),{x,0,50}],x] (* Vincenzo Librandi, Jul 10 2012 *)
LinearRecurrence[{3,-3,1,1,-1},{0,0,2,5,9},40] (* Harvey P. Dale, Jul 04 2013 *)
A201864
a(n) = ((F(n-1)+F(n-2))-1)/2 if F(n) is odd, otherwise a(n) = ((F(n-1)+F(n-2))-2)/2, where F(n) = A000045(n) is the n-th Fibonacci number.
Original entry on oeis.org
0, 0, 0, 1, 2, 3, 6, 10, 16, 27, 44, 71, 116, 188, 304, 493, 798, 1291, 2090, 3382, 5472, 8855, 14328, 23183, 37512, 60696, 98208, 158905, 257114, 416019, 673134, 1089154, 1762288, 2851443, 4613732, 7465175, 12078908, 19544084, 31622992, 51167077, 82790070
Offset: 1
-
[IsOdd(Fibonacci(n)) select (Fibonacci(n)-1)/2 else Fibonacci(n)/2-1: n in [1..41]]; // Bruno Berselli, Dec 14 2011
-
a:= n-> (Matrix(5, (i, j)-> `if`(i=j-1, 1, `if`(i=5,
[-1, -1, 1, 1, 1][j], 0)))^n. <<-1, 0, 0, 0, 1>>)[1, 1]:
seq(a(n), n=1..50); # Alois P. Heinz, Dec 13 2011
-
CoefficientList[Series[x^3*(1+x)/((1-x)(1+x+x^2)(1-x-x^2)),{x,0,30}],x] (* Vincenzo Librandi, Mar 20 2012 *)
A209231
Number of binary words of length n such that there is at least one 0 and every run of consecutive 0's is of length >= 4.
Original entry on oeis.org
0, 0, 0, 0, 1, 3, 6, 10, 15, 22, 33, 51, 80, 125, 193, 295, 449, 684, 1045, 1600, 2451, 3752, 5738, 8770, 13403, 20488, 31326, 47903, 73251, 112003, 171244, 261812, 400284, 612008, 935736, 1430709, 2187495, 3344566, 5113646, 7818463, 11953990
Offset: 0
a(5) = 3 because we have: {0,0,0,0,0}, {0,0,0,0,1}, {1,0,0,0,0}.
-
nn=40; a=x^4/(1-x); CoefficientList[Series[(a+1)/((1-a x/(1-x)))*1/(1-x)-1/(1-x), {x,0,nn}], x]
Comments