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A047859 a(n) = T(2, n), array T given by A047858. 4
1, 4, 11, 27, 63, 143, 319, 703, 1535, 3327, 7167, 15359, 32767, 69631, 147455, 311295, 655359, 1376255, 2883583, 6029311, 12582911, 26214399, 54525951, 113246207, 234881023, 486539263, 1006632959, 2080374783, 4294967295, 8858370047, 18253611007, 37580963839 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

n-th difference of a(n), a(n-1), ..., a(0) is (3, 4, 5, ...).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

FORMULA

Main diagonal of the array defined by: T(0, j)=j+1 j>=0, T(i, 0)=i+1 i>=0, T(i, j)=T(i-1, j-1)+T(i-1, j)+1. a(n)=(n+4)*2^(n-1)-1. - Benoit Cloitre, Jun 17 2003

a(0)=1, a(1)=4, a(2)=11, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - Vincenzo Librandi, Sep 28 2011

G.f.: (1-x-x^2) / ((1-x)*(1-2*x)^2). - Colin Barker, Aug 24 2016

PROG

(MAGMA) [(n+4)*2^(n-1)-1: n in [0..30]]; // Vincenzo Librandi, Sep 28 2011

(PARI) Vec((1-x-x^2)/((1-x)*(1-2*x)^2) + O(x^40)) \\ Colin Barker, Aug 24 2016

CROSSREFS

Sequence in context: A036890 A000253 A276691 * A100335 A080869 A137229

Adjacent sequences:  A047856 A047857 A047858 * A047860 A047861 A047862

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 27 21:47 EST 2020. Contains 332310 sequences. (Running on oeis4.)