A028992 Even 9-gonal (or enneagonal) numbers.

0, 24, 46, 154, 204, 396, 474, 750, 856, 1216, 1350, 1794, 1956, 2484, 2674, 3286, 3504, 4200, 4446, 5226, 5500, 6364, 6666, 7614, 7944, 8976, 9334, 10450, 10836, 12036, 12450, 13734, 14176, 15544, 16014, 17466, 17964, 19500, 20026, 21646, 22200, 23904

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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) = (1/2)*(28*(n-1)^2 + 60*(n-1) + 33 + (14*(n-1)+15)*(-1)^(n-1)).

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.: -2*x*(3*x^3+30*x^2+11*x+12) / ((x-1)^3*(x+1)^2). - Colin Barker, May 30 2015

Prog

(Magma) [(1/2)*(28*(n-1)^2 + 60*(n-1) + 33 + (14*(n-1)+15)*(-1)^(n-1)): n in [0..40]]; // Vincenzo Librandi, Aug 19 2011
(PARI) concat(0, Vec(-2*x*(3*x^3+30*x^2+11*x+12)/((x-1)^3*(x+1)^2) + O(x^100))) \\ Colin Barker, May 30 2015

Crossrefs

Cf. A001106.

Cf. A014642, A028991, A028994.

Sequence in context: A226327 A063323 A154590 * A220515 A215148 A040552

Adjacent sequences: A028989 A028990 A028991 * A028993 A028994 A028995

Keyword

nonn,easy

Author

Patrick De Geest

Extensions

0 inserted, offset and formula corrected by Omar E. Pol, Aug 19 2011

Status

approved