The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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 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(n-1)-6*a(n-2)+4*a(n-3)-a(n-4); G.f.: (1+14*x+9*x^2)/(x-1)^4. - R. J. Mathar, Sep 19 2010 a(n) = Sum_{i=1..2n-1} (n^2 + n*i - i). - Wesley Ivan Hurt, Sep 29 2014 From Amiram Eldar, Jun 28 2020: (Start) Sum_{n>=0} 1/a(n) = Pi^2/4 - log(4). Sum_{n>=0} (-1)^n/a(n) = 2*G + log(2) - Pi/2, where G is the Catalan constant (A006752). (End) 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 23 09:01 EDT 2020. Contains 337298 sequences. (Running on oeis4.)