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A104522 Expansion of (-1+x+3*x^2-x^3)/((x+1)(3*x-1)(x-1)^2). 1
1, 3, 7, 19, 53, 155, 459, 1371, 4105, 12307, 36911, 110723, 332157, 996459, 2989363, 8968075, 26904209, 80712611, 242137815, 726413427, 2179240261, 6537720763, 19613162267, 58839486779, 176518460313, 529555380915, 1588666142719, 4765998428131 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A floretion-generated sequence relating to A081250 (Numbers n such that A081249(m)/m^2 has a local minimum for m = n).

Binomial transform starts: 1, 4, 14, 50, 184, 696, 2688, 10528, 41600, 165248, ... - Wesley Ivan Hurt, Sep 12 2014

LINKS

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,3).

FORMULA

a(n) = (1/8) * (5*3^n + 4*(n+1) - (-1)^n). - Ralf Stephan, Nov 13 2010.

a(n+2) - 2a(n+1) + a(n) = A081250(n+1) - A081250(n).

a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3)+3*a(n-4). - Wesley Ivan Hurt, Sep 12 2014

MAPLE

A104522:=n->(5*3^n+4*(n+1)-(-1)^n)/8: seq(A104522(n), n=0..30); # Wesley Ivan Hurt, Sep 12 2014

MATHEMATICA

CoefficientList[Series[(-1 + x + 3 x^2 - x^3)/((x + 1) (3*x - 1) (x - 1)^2), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 12 2014 *)

PROG

Floretion Algebra Multiplication Program, FAMP Code: 1famforrokseq[ - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki']

(MAGMA) [(5*3^n+4*(n+1)-(-1)^n)/8 : n in [0..30]]; // Wesley Ivan Hurt, Sep 12 2014

CROSSREFS

Cf. A081250, A105792.

Sequence in context: A183124 A078481 A183122 * A175533 A115760 A183115

Adjacent sequences:  A104519 A104520 A104521 * A104523 A104524 A104525

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Apr 20 2005

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.