A104522 Expansion of (-1+x+3*x^2-x^3)/((x+1)(3*x-1)(x-1)^2).

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

Offset: 0

Author

Creighton Dement, Apr 20 2005

Keywords

• nonn
• easy

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

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

Links

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

Crossrefs

Cf. A081250, A105792.

Programs

Magma

[(5*3^n+4*(n+1)-(-1)^n)/8 : n in [0..30]]; // 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 *)

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