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A062124 Fourth column of A046741. 2
3, 26, 94, 234, 473, 838, 1356, 2054, 2959, 4098, 5498, 7186, 9189, 11534, 14248, 17358, 20891, 24874, 29334, 34298, 39793, 45846, 52484, 59734, 67623, 76178, 85426, 95394, 106109, 117598, 129888, 143006, 156979, 171834, 187598, 204298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, (2.3.14).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: (3 + 14*x + 8*x^2 + 2*x^3)/(1-x)^4. Generally, g.f. for k-th column of A046741 is coefficient of y^k in expansion of (1-y)/((1-y-y^2)*(1-y) - (1+y)*x).

From G. C. Greubel, Jan 31 2019: (Start)

a(n) = (6 + 19*n + 18*n^2 + 9*n^3)/2.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

E.g.f.: (6 + 46*x + 45*x^2 + 9*x^3)*exp(x)/2. (End)

MATHEMATICA

Table[(6+19*n+18*n^2+9*n^3)/2, {n, 0, 40}] (* G. C. Greubel, Jan 31 2019 *)

PROG

(PARI) vector(40, n, n--; (6+19*n+18*n^2+9*n^3)/2) \\ G. C. Greubel, Jan 31 2019

(MAGMA) [(6+19*n+18*n^2+9*n^3)/2: n in [0..40]]; // G. C. Greubel, Jan 31 2019

(Sage) [(6+19*n+18*n^2+9*n^3)/2 for n in range(40)] # G. C. Greubel, Jan 31 2019

(GAP) List([0..40], n -> (6+19*n+18*n^2+9*n^3)/2); # G. C. Greubel, Jan 31 2019

CROSSREFS

Cf. dumbbells: A002940, A002941, A002889, A046741, A055608, A062123-A062127.

Sequence in context: A269342 A292001 A211622 * A169832 A322300 A100606

Adjacent sequences:  A062121 A062122 A062123 * A062125 A062126 A062127

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jun 04 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

STATUS

approved

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Last modified April 11 06:11 EDT 2021. Contains 342886 sequences. (Running on oeis4.)