A204555 The number of subsets of the numbers {1,2,3...,n} consisting of at most 3 elements and at most two of those are even.
1, 2, 4, 8, 15, 26, 41, 63, 89, 126, 166, 222, 279, 358, 435, 541, 641, 778, 904, 1076, 1231, 1442, 1629, 1883, 2105, 2406, 2666, 3018, 3319, 3726, 4071, 4537, 4929, 5458, 5900, 6496, 6991, 7658, 8209, 8951, 9561, 10382, 11054, 11958, 12695, 13686, 14491
Offset: 0
Examples
a(7) = ((14*7^3+15*7^2+49*7+111)-(3*7^2-15*7+15)(-1)^7)/96 = 63.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
Programs
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Maple
seq(binomial(n, 3)+binomial(n, 2)+binomial(n, 1)+binomial(n, 0)- binomial(floor(n/2), 3) , n=0..29);
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Mathematica
Table[Total[Table[Binomial[n,i],{i,0,3}]]-Binomial[Floor[n/2],3],{n,0,60}] (* or *) LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,2,4,8,15,26,41},60] (* Harvey P. Dale, Apr 17 2012 *)
Formula
a(n) = {(14*n^3+15*n^2+49*n+111)-(3*n^2-15*n+15)(-1)^n}/96.
G.f.: ( 1+x-x^2+x^3+4*x^4+2*x^5-x^6 ) / ( (1+x)^3*(x-1)^4 ). - R. J. Mathar, Jan 19 2012
a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=15, a(5)=26, a(6)=41, a(n)=a(n-1)+ 3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7). - Harvey P. Dale, Apr 17 2012
Extensions
More terms from Harvey P. Dale, Apr 17 2012
Comments