A014833 a(n) = 2^n - n*(n+1)/2.
1, 1, 1, 2, 6, 17, 43, 100, 220, 467, 969, 1982, 4018, 8101, 16279, 32648, 65400, 130919, 261973, 524098, 1048366, 2096921, 4194051, 8388332, 16776916, 33554107, 67108513, 134217350, 268435050, 536870477, 1073741359, 2147483152, 4294966768, 8589934031, 17179868589
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..240
- Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
Programs
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Magma
[2^n - n*(n+1)/2: n in [0..50]]; // Vincenzo Librandi, Apr 25 2011
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Maple
seq(2^n-n*(n+1)/2, n=0..30); # Zerinvary Lajos, Jul 01 2007
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Mathematica
Table[2^n-n (n+1)/2,{n,0,50}] (* or *) LinearRecurrence[{5,-9,7,-2},{1,1,1,2},50] (* Harvey P. Dale, May 12 2011 *)
Formula
From Harvey P. Dale, May 12 2011: (Start)
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(0)=1, a(1)=1, a(2)=1, a(3)=2.
G.f.: 1/(1-2*x) + 1/(-1+x)^3 + 1/(-1+x)^2. (End)
a(n) = A331105(n,n) for n>0. - Alois P. Heinz, Jan 16 2020
E.g.f.: exp(x)*(exp(x) - x*(x + 2)/2). - Elmo R. Oliveira, Mar 06 2025