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 A084634 Binomial transform of 1, 1, 1, 2, 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.: (1-3*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 Cf. A000225, A000325, Sequence in context: A351644 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 June 9 11:22 EDT 2023. Contains 363178 sequences. (Running on oeis4.)