A028993 Odd 10-gonal (or decagonal) numbers.

1, 27, 85, 175, 297, 451, 637, 855, 1105, 1387, 1701, 2047, 2425, 2835, 3277, 3751, 4257, 4795, 5365, 5967, 6601, 7267, 7965, 8695, 9457, 10251, 11077, 11935, 12825, 13747, 14701, 15687, 16705, 17755, 18837, 19951, 21097, 22275, 23485, 24727, 26001, 27307, 28645

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Decagonal Number.

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

Formula

a(n) = (2*n+1)*(8*n+1). - N. J. A. Sloane

G.f.: -(7*x^2+24*x+1)/(x-1)^3. - Colin Barker, Nov 18 2012

Sum_{n>=0} 1/a(n) = (4*log(2) + (sqrt(2)+1)*Pi + 2*sqrt(2)*log(1+sqrt(2)))/12. - Amiram Eldar, Feb 27 2022

From Elmo R. Oliveira, Oct 27 2024: (Start)

E.g.f.: exp(x)*(1 + 26*x + 16*x^2).

a(n) = A005408(n)*A017077(n) = A001107(2*n+1).

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

Maple

A028993:=n->(2*n+1)*(8*n+1): seq(A028993(n), n=0..100); # Wesley Ivan Hurt, Apr 26 2017

Mathematica

CoefficientList[Series[-(7 x^2 + 24 x + 1)/(x - 1)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Select[PolygonalNumber[10, Range[100]], OddQ] (* or *) LinearRecurrence[{3, -3, 1}, {1, 27, 85}, 50] (* Harvey P. Dale, May 03 2023 *)

Prog

(Magma) [(2*n+1)*(8*n+1): n in [0..60]]; // Vincenzo Librandi, Oct 18 2013
(PARI) a(n)=(2*n+1)*(8*n+1) \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A001107, A005408, A017077, A028994.

Sequence in context: A036925 A281090 A260052 * A262367 A007266 A098320

Adjacent sequences: A028990 A028991 A028992 * A028994 A028995 A028996

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved