A062124 Fourth column of A046741.

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

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 *)
LinearRecurrence[{4, -6, 4, -1}, {3, 26, 94, 234}, 40] (* Harvey P. Dale, Feb 20 2022 *)

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