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A236257
a(n) = 2*n^2 - 7*n + 9.
2
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
OFFSET
0,1
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.
LINKS
W. Burrows, C. Tuffley, Maximising common fixtures in a round robin tournament with two divisions, arXiv preprint arXiv:1502.06664 [math.CO], 2015.
FORMULA
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: -(18*x^2-23*x+9) / (x-1)^3. - Colin Barker, Jan 21 2014
EXAMPLE
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.
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 *)
PROG
(PARI) Vec(-(18*x^2-23*x+9)/(x-1)^3 + O(x^100)) \\ Colin Barker, Jan 21 2014
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, Jan 21 2014
STATUS
approved