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

1,2

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).

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

Mathematica

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

Prog

(Magma) [(1/6)*(10*n^3-9*n^2+5*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (10*n^3-9*n^2+5*n)/6) \\ G. C. Greubel, Nov 08 2018

Crossrefs

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

Sequence in context: A236370 A273744 A133547 * A106598 A279128 A293038

Adjacent sequences: A100176 A100177 A100178 * A100180 A100181 A100182

Keyword

nonn,easy

Author

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

Status

approved