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A084634
Binomial transform of 1, 1, 1, 2, 2, 2, 2, 2, ...
8
1, 2, 4, 9, 21, 48, 106, 227, 475, 978, 1992, 4029, 8113, 16292, 32662, 65415, 130935, 261990, 524116, 1048385, 2096941, 4194072, 8388354, 16776939, 33554131, 67108538, 134217376, 268435077, 536870505, 1073741388, 2147483182, 4294966799, 8589934063
OFFSET
0,2
COMMENTS
Partial sums of A000325.
FORMULA
a(n) = 2^(n+1) - (n^2 + n + 2)/2.
a(n) = 1 + n + n*(n-1)/2 + 2*Sum_{k=3..n} C(n, k).
O.g.f.: (1-3*x+3*x^2)/((1-2*x)*(1-x)^3). - R. J. Mathar, Apr 07 2008
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4). - R. J. Mathar, Apr 07 2008
a(n) = Sum_{i=0..n} (2^i - i). - Ctibor O. Zizka, Oct 15 2010
a(n) = A000225(n+1) - binomial(n+1,2). - G. C. Greubel, Mar 18 2023
MAPLE
A084634:=n->2^(n+1) - (n^2 +n +2)/2; seq(A084634(n), n=0..50); # Wesley Ivan Hurt, Jan 31 2014
MATHEMATICA
LinearRecurrence[{5, -9, 7, -2}, {1, 2, 4, 9}, 50] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2012 *)
PROG
(Sage) [2^(n+1)-1-binomial(n+1, 2) for n in range(52)] # Zerinvary Lajos, May 29 2009
(Magma) [2^(n+1)-1-Binomial(n+1, 2): n in [0..50]]; // G. C. Greubel, Mar 18 2023
CROSSREFS
Sequence in context: A351644 A027711 A307548 * A137256 A051164 A182904
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jun 06 2003
STATUS
approved