A321988 - OEIS

A321988

Number of integer triples (x,y,z) with x,y,z>0 and 4*x+6*y+3*n*z < 12*n.

0, 0, 4, 13, 27, 47, 70, 102, 135, 178, 220, 275, 327, 393, 454, 532, 603, 692, 772, 873, 963, 1075, 1174, 1298, 1407, 1542, 1660, 1807, 1935, 2093, 2230, 2400, 2547, 2728, 2884, 3077, 3243, 3447, 3622, 3838, 4023

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OFFSET

0,3

COMMENTS

In the Comtet formula the round() must not just encompass the (21n^2+6(-)^n)/8 but also the term -n(17+(-)^n)/4 to be correct. See the Maple code.

REFERENCES

L. Comtet, Advanced Combinatorics (Reidel 1974), page 122, Exercise #19(3)

LINKS

Table of n, a(n) for n=0..40.

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

FORMULA

G.f. -x^2*(4+9*x+10*x^2+11*x^3+5*x^4+3*x^5) / ( (x^2+1)*(1+x)^2*(x-1)^3 ).

MAPLE

A321988 := proc(n)

2-n*(17+(-1)^n)/4 +(21*n^2+6*(-1)^n)/8;

round(%) ;

end proc:

seq(A321988(n), n=0..30) ;

CROSSREFS

Sequence in context: A316616 A119652 A147875 * A108753 A024970 A079430

Adjacent sequences: A321985 A321986 A321987 * A321989 A321990 A321991

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Nov 23 2018

STATUS

approved