login
Number of nonseparable tree-rooted planar maps with n + 3 edges and 4 vertices.
(Formerly M3697)
4

%I M3697 #22 Apr 05 2021 21:37:06

%S 4,75,604,3150,12480,40788,115500,292578,677820,1459315,2954952,

%T 5679700,10438272,18449760,31511880,52213596,84206100,132543411,

%U 204105220,308116050,456776320,666022500,956435220,1354315950,1892954700,2614113099,3569749200,4824012424

%N Number of nonseparable tree-rooted planar maps with n + 3 edges and 4 vertices.

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

%H Andrew Howroyd, <a href="/A006412/b006412.txt">Table of n, a(n) for n = 1..1000</a>

%H T. R. S. Walsh and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

%F a(n) = 4 * binomial(n + 4, 5) + 51 * binomial(n + 4, 6) + 163 * binomial(n + 4, 7) + 194 * binomial(n + 4, 8) + 78 * binomial(n + 4, 9). - _Sean A. Irvine_, Apr 03 2017

%F a(n) = binomial(n+5,6)*(n + 3)*(13*n^2 + 57*n + 14)/84. - _Andrew Howroyd_, Apr 05 2021

%o (PARI) a(n) = {binomial(n+5,6)*(n + 3)*(13*n^2 + 57*n + 14)/84} \\ _Andrew Howroyd_, Apr 05 2021

%Y Column 4 of A342984.

%Y Cf. A006411, A006413.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E Terms a(11) and beyond from _Andrew Howroyd_, Apr 05 2021