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A140787 Expansion of 1 / ( (1+x)*(2*x+1)*(-1+2*x)^2 ). 1
1, 1, 7, 9, 39, 57, 199, 313, 967, 1593, 4551, 7737, 20935, 36409, 94663, 167481, 422343, 757305, 1864135, 3378745, 8155591, 14913081, 35418567, 65244729, 152859079, 283348537, 656175559, 1222872633, 2803659207, 5249404473 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index to sequences with linear recurrences with constant coefficients, signature (1,6,-4,-8).

FORMULA

a(n) = 2^n*(n/3+11/18) + (-1)^n* (2^(n-1)-1/9).

a(2n)-2a(2n-1) = A002450(n+1).

a(n)+a(n+1) = A134353(n+1). - R. J. Mathar, Nov 10 2013

MATHEMATICA

max = 40; j[n_] := (2^n-(-1)^n)/3; jj = Table[{j[n], -j[n]}, {n, 0, max+2, 2}] // Flatten; a[0] = 1; a[n_] := a[n] = 2*a[n-1] + jj[[n+3]]; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Sep 30 2013 *)

PROG

(MAGMA) [2^n*(n/3+11/18) + (-1)^n* (2^(n-1)-1/9): n in [0..40]]; // Vincenzo Librandi, Aug 08 2011

CROSSREFS

Cf. A092808, A094359, A140505.

Sequence in context: A083203 A082536 A057590 * A032695 A007449 A189053

Adjacent sequences:  A140784 A140785 A140786 * A140788 A140789 A140790

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 14 2008

EXTENSIONS

Better name from R. J. Mathar, Jul 02 2011

Edited by Ralf Stephan, Nov 10 2013

STATUS

approved

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Last modified November 27 04:47 EST 2014. Contains 250155 sequences.