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