

A139757


a(n) = (n+1)*(2n+1)^2.


4



1, 18, 75, 196, 405, 726, 1183, 1800, 2601, 3610, 4851, 6348, 8125, 10206, 12615, 15376, 18513, 22050, 26011, 30420, 35301, 40678, 46575, 53016, 60025, 67626, 75843, 84700, 94221, 104430, 115351, 127008, 139425, 152626, 166635, 181476
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OFFSET

0,2


COMMENTS

Also the detour index of the (n+1)antiprism graph and (n+1)cocktail party graphs for n>=2.  Eric W. Weisstein, Jul 15 2011 and Dec 20 2017


LINKS

Table of n, a(n) for n=0..35.
Eric Weisstein's World of Mathematics, Antiprism Graph
Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Detour Index
Index entries for linear recurrences with constant coefficients, signature (4,6,4,1).


FORMULA

a(n) = (2n+1) * A000217(2n+1).
a(n) = 4*a(n1)6*a(n2)+4*a(n3)a(n4); G.f.: (1+14*x+9*x^2)/(x1)^4.  R. J. Mathar, Sep 19 2010
a(n) = Sum_{i=1..2n1} (n^2 + n*i  i).  Wesley Ivan Hurt, Sep 29 2014


MAPLE

A139757:=n>(n+1)*(2*n+1)^2: seq(A139757(n), n=0..30); # Wesley Ivan Hurt, Sep 29 2014


MATHEMATICA

Table[(n + 1) (2 n + 1)^2, {n, 0, 30}] (* Wesley Ivan Hurt, Sep 29 2014 *)
LinearRecurrence[{4, 6, 4, 1}, {18, 75, 196, 405}, {0, 20}] (* Eric W. Weisstein, Dec 20 2017 *)
CoefficientList[Series[(1 + 14 x + 9 x^2)/(1 + x)^4, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 20 2017 *)


PROG

(MAGMA) [(n+1)*(2*n+1)^2 : n in [0..30]]; // Wesley Ivan Hurt, Sep 29 2014
(PARI) a(n) = (n+1)*(2*n+1)^2; \\ Altug Alkan, Dec 20 2017


CROSSREFS

Cf. A000217, A006254.
Sequence in context: A022145 A284659 A143666 * A285918 A262402 A296363
Adjacent sequences: A139754 A139755 A139756 * A139758 A139759 A139760


KEYWORD

easy,nonn


AUTHOR

Odimar Fabeny, May 19 2008


EXTENSIONS

Missing a(0) inserted by R. J. Mathar, Sep 19 2010


STATUS

approved



