A236257 a(n) = 2*n^2 - 7*n + 9.

9, 4, 3, 6, 13, 24, 39, 58, 81, 108, 139, 174, 213, 256, 303, 354, 409, 468, 531, 598, 669, 744, 823, 906, 993, 1084, 1179, 1278, 1381, 1488, 1599, 1714, 1833, 1956, 2083, 2214, 2349, 2488, 2631, 2778, 2929, 3084, 3243, 3406, 3573, 3744, 3919, 4098, 4281, 4468

Offset: 0

Author

Vladimir Shevelev, Jan 21 2014

Keywords

• nonn
• easy

Comments

If zero polygonal numbers are ignored, then for n >= 3, the a(n)-th n-gonal number is a sum of the (a(n)-1)-th n-gonal number and the (2*n-3)-th n-gonal number.

Examples

			a(7)=58. This means that the 58th heptagonal number 8323 (cf. A000566) is a sum of two heptagonal numbers. We have 8323 = 8037 + 286 with indices in A000566 58,57,11.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000
• W. Burrows, C. Tuffley, Maximising common fixtures in a round robin tournament with two divisions, arXiv preprint arXiv:1502.06664 [math.CO], 2015.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051624, A051682, A051865-A051876, A152948.

Programs

Mathematica

Table[2 n^2 - 7 n + 9, {n, 0, 48}] (* Michael De Vlieger, Apr 19 2015 *)
LinearRecurrence[{3,-3,1},{9,4,3},50] (* Harvey P. Dale, Nov 24 2017 *)

PARI

Vec(-(18*x^2-23*x+9)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jan 21 2014

Formula

From Colin Barker, Jan 21 2014: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: -(18*x^2 - 23*x + 9)/(x-1)^3. (End)

E.g.f.: exp(x)*(9 - 5*x + 2*x^2). - Elmo R. Oliveira, Nov 13 2024