A100179 Structured heptagonal diamond numbers (vertex structure 5).

1, 9, 34, 86, 175, 311, 504, 764, 1101, 1525, 2046, 2674, 3419, 4291, 5300, 6456, 7769, 9249, 10906, 12750, 14791, 17039, 19504, 22196, 25125, 28301, 31734, 35434, 39411, 43675, 48236, 53104

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. A004126 = alternate vertex; A000447 = structured diamonds; A100145 for more on structured numbers.

Programs

Magma

[(1/6)*(10*n^3-9*n^2+5*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011

Mathematica

Table[(10n^3-9n^2+5n)/6,{n,40}] (* Harvey P. Dale, Oct 28 2018 *)

PARI

vector(40, n, (10*n^3-9*n^2+5*n)/6) \\ G. C. Greubel, Nov 08 2018

Formula

a(n) = (1/6)*(10*n^3 - 9*n^2 + 5*n).

G.f.: x*(1 + 5*x + 4*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). - Harvey P. Dale, Oct 28 2018

E.g.f.: (6*x + 21*x^2 + 10*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018