A153785 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.

0, 5, 35, 90, 170, 275, 405, 560, 740, 945, 1175, 1430, 1710, 2015, 2345, 2700, 3080, 3485, 3915, 4370, 4850, 5355, 5885, 6440, 7020, 7625, 8255, 8910, 9590, 10295, 11025, 11780, 12560, 13365, 14195, 15050, 15930, 16835, 17765

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = (25*n^2 - 15*n)/2 = A000566(n)*5.

a(n) = 25*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

From G. C. Greubel, Aug 28 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 5*x*(1 + 4*x)/(1 - x)^3.

E.g.f.: (5/2)*x*(2 + 5*x)*exp(x). (End)

Mathematica

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 5, 8!, 25}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 03 2009 *)
Table[5*n*(5*n - 3)/2, {n, 0, 25}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 5, 35}, 25] (* G. C. Greubel, Aug 28 2016 *)
5*PolygonalNumber[7, Range[0, 50]] (* Harvey P. Dale, Dec 02 2025 *)

Prog

(PARI) a(n) = 5*n*(5*n-3)/2; \\ Michel Marcus, Aug 28 2016

Crossrefs

Cf. A000566, A153784, A154786.

Sequence in context: A145920 A356179 A356132 * A369812 A090294 A162540

Adjacent sequences: A153782 A153783 A153784 * A153786 A153787 A153788

Keyword

nonn,easy

Author

Omar E. Pol, Jan 07 2009

Status

approved