A124089 a(n) = binomial(n,6)-1.
0, 6, 27, 83, 209, 461, 923, 1715, 3002, 5004, 8007, 12375, 18563, 27131, 38759, 54263, 74612, 100946, 134595, 177099, 230229, 296009, 376739, 475019, 593774, 736280, 906191, 1107567, 1344903, 1623159, 1947791, 2324783, 2760680, 3262622
Offset: 6
Links
- Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
Programs
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Magma
[Binomial(n,6)-1 : n in [6..40]]; // Wesley Ivan Hurt, Dec 27 2023
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Maple
[seq(binomial(n,6)-1,n=6..42)];
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Mathematica
Binomial[Range[6,40],6]-1 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,6,27,83,209,461,923},40] (* Harvey P. Dale, Dec 26 2015 *)
Formula
a(n) = A000579(n)-1.
a(0)=0, a(1)=6, a(2)=27, a(3)=83, a(4)=209, a(5)=461, a(6)=923, a(n)= 7*a(n-1)- 21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+ a(n-7). - Harvey P. Dale, Dec 26 2015