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A084634 Binomial transform of 1,1,1,2,2,2,2,... 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A000325.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

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.: (1-3x+3x^2)/((1-2x)(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

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) [gaussian_binomial(n, 1, 2)-binomial(n, 2) for n in range(1, 32)] # Zerinvary Lajos, May 29 2009

CROSSREFS

Sequence in context: A061439 A027711 A307548 * A137256 A051164 A182904

Adjacent sequences:  A084631 A084632 A084633 * A084635 A084636 A084637

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jun 06 2003

STATUS

approved

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Last modified September 22 01:44 EDT 2020. Contains 337275 sequences. (Running on oeis4.)