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
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).
Programs
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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 *) -
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
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