A100189 Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.

1, 6, 27, 92, 245, 546, 1071, 1912, 3177, 4990, 7491, 10836, 15197, 20762, 27735, 36336, 46801, 59382, 74347, 91980, 112581, 136466, 163967, 195432, 231225, 271726, 317331, 368452, 425517, 488970, 559271, 636896

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A000578, A096000, A051673, A005915, A100186, A100187 - "equatorial" structured anti-diamonds; A100188 - "polar" structured meta-anti-diamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(4*n^4-12*n^3+20*n^2-6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

Mathematica

Table[(4n^4-12n^3+20n^2-6n)/6,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{1,6,27,92,245},40] (* Harvey P. Dale, Jul 05 2011 *)

Formula

a(n) = (1/6)*(4*n^4-12*n^3+20*n^2-6*n).

a(1)=1, a(2)=6, a(3)=27, a(4)=92, a(5)=245, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Jul 05 2011

G.f.: x*(1+x)*(1+7*x^2)/(1-x)^5. - Colin Barker, Jan 19 2012