A028991 Odd 9-gonal (or enneagonal) numbers.

1, 9, 75, 111, 261, 325, 559, 651, 969, 1089, 1491, 1639, 2125, 2301, 2871, 3075, 3729, 3961, 4699, 4959, 5781, 6069, 6975, 7291, 8281, 8625, 9699, 10071, 11229, 11629, 12871, 13299, 14625, 15081, 16491, 16975, 18469, 18981, 20559, 21099, 22761, 23329, 25075

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Nonagonal Number

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

a(n) = (28*n^2 + 4*n + 1 + (14*n+1)*(-1)^n)/2.

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>4. - Colin Barker, May 30 2015

G.f.: -(19*x^4+20*x^3+64*x^2+8*x+1) / ((x-1)^3*(x+1)^2). - Colin Barker, May 30 2015

Mathematica

Select[PolygonalNumber[9, Range[100]], OddQ] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {1, 9, 75, 111, 261}, 50] (* Harvey P. Dale, Dec 27 2020 *)

Prog

(PARI) Vec(-(19*x^4+20*x^3+64*x^2+8*x+1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, May 30 2015

Crossrefs

Cf. A001106, A028992.

Sequence in context: A190984 A001716 A231910 * A249396 A102094 A321234

Adjacent sequences: A028988 A028989 A028990 * A028992 A028993 A028994

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved