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A055232 Expansion of (1+2*x+3*x^2)/((1-x)^3*(1-x^2)). 8
1, 5, 16, 36, 69, 117, 184, 272, 385, 525, 696, 900, 1141, 1421, 1744, 2112, 2529, 2997, 3520, 4100, 4741, 5445, 6216, 7056, 7969, 8957, 10024, 11172, 12405, 13725, 15136, 16640, 18241, 19941, 21744, 23652, 25669, 27797, 30040, 32400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of (w,x,y} having all terms in {0..n} and w<=floor((x+y)/2). [Clark Kimberling, Jun 02 2012]

First differences are in A212959. - Wesley Ivan Hurt, Apr 16 2016

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.28(c), y_3.

LINKS

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

FORMULA

G.f.: (1+2*x+3*x^2)/((1-x)^3*(1-x^2)).

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). [Clark Kimberling, Jun 02 2012]

a(n) = (7+(-1)^n+16*n+14*n^2+4*n^3)/8. [Eric W. Weisstein, Apr 04 2013]

a(n) = ((n+1)^3 + ceiling((n+1)/2)^2 + floor((n+1)/2)^2)/2. - Wesley Ivan Hurt, Apr 15 2016

E.g.f.: ((7 + 34*x + 26*x^2 + 4*x^3)*exp(x) + exp(-x))/8. - Ilya Gutkovskiy, Apr 16 2016

MAPLE

A055232:=n->(7+(-1)^n+16*n+14*n^2+4*n^3)/8: seq(A055232(n), n=0..100); # Wesley Ivan Hurt, Apr 15 2016

MATHEMATICA

Table[(7 + (-1)^n + 16*n + 14*n^2 + 4*n^3)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Apr 15 2016 *)

PROG

(MAGMA) [(7+(-1)^n+16*n+14*n^2+4*n^3)/8 : n in [0..100]]; // Wesley Ivan Hurt, Apr 15 2016

(PARI) lista(nn) = for(n=0, nn, print1((7+(-1)^n+16*n+14*n^2+4*n^3)/8, ", ")); \\ Altug Alkan, Apr 16 2016

CROSSREFS

Cf. A212959.

Sequence in context: A108966 A184635 A072333 * A211806 A001210 A264552

Adjacent sequences:  A055229 A055230 A055231 * A055233 A055234 A055235

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jul 05 2000

STATUS

approved

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Last modified October 16 00:50 EDT 2018. Contains 316252 sequences. (Running on oeis4.)