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A028991
Odd 9-gonal (or enneagonal) numbers.
2
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
Eric Weisstein's World of Mathematics, Nonagonal Number
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
Sequence in context: A001716 A372843 A231910 * A249396 A102094 A321234
KEYWORD
nonn,easy
STATUS
approved