

A100188


Polar structured metaantidiamond numbers, the nth number from a polar structured ngonal antidiamond number sequence.


15



1, 6, 27, 84, 205, 426, 791, 1352, 2169, 3310, 4851, 6876, 9477, 12754, 16815, 21776, 27761, 34902, 43339, 53220, 64701, 77946, 93127, 110424, 130025, 152126, 176931, 204652, 235509, 269730, 307551, 349216
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OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5, 10, 10, 5, 1).


FORMULA

a(n) = (1/6)*(2*n^4  2*n^2 + 6*n).
G.f.: x*(1 + x + 7*x^2  x^3)/(1x)^5.  Colin Barker, Apr 16 2012
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5); a(1)=1, a(2)=6, a(3)=27, a(4)=84, a(5)=205.  Harvey P. Dale, May 11 2016
E.g.f.: (3*x + 6*x^2 + 6*x^3 + x^4)*exp(x)/3.  G. C. Greubel, Nov 08 2018


EXAMPLE

There are no 1 or 2gonal antidiamonds, so 1 and (2n+2) are the first and second terms since all the sequences begin as such.


MATHEMATICA

Table[(2n^42n^2+6n)/6, {n, 40}] (* or *) LinearRecurrence[{5, 10, 10, 5, 1}, {1, 6, 27, 84, 205}, 40] (* Harvey P. Dale, May 11 2016 *)


PROG

(MAGMA) [(1/6)*(2*n^42*n^2+6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (n^4 n^2 +3*n)/3) \\ G. C. Greubel, Nov 08 2018


CROSSREFS

Cf. A000578, A000447, A004466, A007588, A063521, A062523  "polar" structured antidiamonds; A100189  "equatorial" structured metaantidiamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.
Sequence in context: A217365 A124089 A250283 * A131985 A125196 A100189
Adjacent sequences: A100185 A100186 A100187 * A100189 A100190 A100191


KEYWORD

nonn,easy


AUTHOR

James A. Record (james.record(AT)gmail.com), Nov 07 2004


STATUS

approved



