A006417 Number of loopless rooted planar maps with 4 faces and n vertices and no isthmuses. (Formerly M5091)

1, 20, 131, 469, 1262, 2862, 5780, 10725, 18647, 30784, 48713, 74405, 110284, 159290, 224946, 311429, 423645, 567308, 749023, 976373, 1258010, 1603750, 2024672, 2533221, 3143315, 3870456, 4731845, 5746501, 6935384, 8321522, 9930142, 11788805, 13927545, 16379012

Offset

2,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Andrew Howroyd, Table of n, a(n) for n = 2..1000

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From Colin Barker, Apr 08 2013: (Start)

a(n) = (2160+846*n-1027*n^2-345*n^3+125*n^4+39*n^5+2*n^6)/360.

G.f.: -x^2*(5*x^6-29*x^5+65*x^4-63*x^3+12*x^2+13*x+1) / (x-1)^7. (End)

E.g.f.: exp(x)*(2160 - 360*x - 540*x^2 + 1560*x^3 + 645*x^4 + 69*x^5 + 2*x^6)/360 - 6 - 5*x. - Stefano Spezia, Jul 18 2024

Prog

(PARI) a(n)={if(n<2, 0, (2*n^6 + 39*n^5 + 125*n^4 - 345*n^3 - 1027*n^2 + 846*n + 2160)/360)} \\ Andrew Howroyd, Apr 01 2021

Crossrefs

Column k=4 of A342980.

Sequence in context: A126488 A304507 A005551 * A156392 A374709 A219574

Adjacent sequences: A006414 A006415 A006416 * A006418 A006419 A006420

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Title improved by Sean A. Irvine, Apr 03 2017

Terms a(14) and beyond from Andrew Howroyd, Apr 01 2021

Status

approved