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A100179 Structured heptagonal diamond numbers (vertex structure 5). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 19:19 EDT 2019. Contains 328308 sequences. (Running on oeis4.)