A100187 Structured octagonal anti-diamond numbers (vertex structure 7).

1, 18, 77, 204, 425, 766, 1253, 1912, 2769, 3850, 5181, 6788, 8697, 10934, 13525, 16496, 19873, 23682, 27949, 32700, 37961, 43758, 50117, 57064, 64625, 72826, 81693, 91252, 101529, 112550, 124341, 136928

Offset: 1

Author

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

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Crossrefs

Cf. A063523 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(26*n^3-30*n^2+10*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

Mathematica

Table[(26n^3-30n^2+10n)/6,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,18,77,204},40] (* Harvey P. Dale, Dec 24 2012 *)

PARI

vector(40, n, (13*n^3 -15*n^2 +5*n)/3) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(26*n^3 - 30*n^2 + 10*n).

G.f.: x*(1 + 14*x + 11*x^2)/(1-x)^4. - Colin Barker, Jan 19 2012

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=1, a(2)=18, a(3)=77, a(4)=204. - Harvey P. Dale, Dec 24 2012

E.g.f.: (3*x + 24*x^2 + 13*x^3)*exp(x)/3. - G. C. Greubel, Nov 08 2018