A381109 a(n) = (21*n^2 + 9*n + 2)/2.

1, 16, 52, 109, 187, 286, 406, 547, 709, 892, 1096, 1321, 1567, 1834, 2122, 2431, 2761, 3112, 3484, 3877, 4291, 4726, 5182, 5659, 6157, 6676, 7216, 7777, 8359, 8962, 9586, 10231, 10897, 11584, 12292, 13021, 13771, 14542, 15334, 16147, 16981, 17836, 18712

Offset: 0

Author

Aaron David Fairbanks, Mar 06 2025

Keywords

• nonn
• easy

Comments

A 9-sided figure is obtained by truncating every other corner of a centered hexagonal figure as in A003215; a(n) is the number of dots in such a 9-sided figure with n+1 dots on each side.

Examples

			Illustration of initial terms:
                                            o o o o
                                           o o o o o o
                       o o o              o o o o o o o o
                      o o o o o          o o o o o o o o o o
         o o         o o o o o o o        o o o o o o o o o o
        o o o o       o o o o o o o      o o o o o o o o o o o
  o      o o o o     o o o o o o o o      o o o o o o o o o o o
        o o o o       o o o o o o o      o o o o o o o o o o o
         o o         o o o o o o o        o o o o o o o o o o
                      o o o o o          o o o o o o o o o o
                       o o o              o o o o o o o o
                                           o o o o o o
                                            o o o o
  1         16             52                    109
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A003215, A005892, A381424.

Programs

Mathematica

LinearRecurrence[{3,-3,1},{1,16,52},43] (* James C. McMahon, Mar 07 2025 *)