A227849 a(n) = 2 * floor( 3/14 * n^2) if n even, a(n) = 2 * round( 3/14 * n^2) -1 if n odd.

0, -1, 0, 3, 6, 9, 14, 21, 26, 33, 42, 51, 60, 71, 84, 95, 108, 123, 138, 153, 170, 189, 206, 225, 246, 267, 288, 311, 336, 359, 384, 411, 438, 465, 494, 525, 554, 585, 618, 651, 684, 719, 756, 791, 828, 867, 906, 945, 986, 1029, 1070, 1113, 1158, 1203, 1248

Offset

0,4

Comments

The degrees of the sequence of the G_2 polynomials defined by Bruce Westbury is conjectured to be a(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

B. W. Westbury, Enumeration of non-positive planar trivalent graphs, J. Algebraic Combin. 25 (2007), 357-373, arXiv:math/0507112 [math.CO], 2005.

B. W. Westbury, Finding recurrence relation for a sequence of polynomials, MathOverflow, 15 July 2010.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 1, -2, 1).

Formula

G.f.: (x^8 - 2*x^7 - 2*x^6 - 2*x^3 - 2*x^2 + x) / (x^9 - 2*x^8 + x^7 - x^2 + 2*x - 1).

G.f.: -x * (1 + x) * (1 - 3*x + x^2 - x^3 + x^4 - 3*x^5 + x^6) / ((1 - x)^2 * (1 - x^7)).

a(-n) = a(n). a(n+7) = a(n) + 3*(2*n + 7).

Example

G.f. = -x + 3*x^3 + 6*x^4 + 9*x^5 + 14*x^6 + 21*x^7 + 26*x^8 + 33*x^9 + ...

Mathematica

CoefficientList[Series[(x^8-2*x^7-2*x^6-2*x^3-2*x^2+x)/(x^9-2*x^8+x^7 - x^2+2*x-1), {x, 0, 50}], x] (* G. C. Greubel, Aug 08 2018 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 1, -2, 1}, {0, -1, 0, 3, 6, 9, 14, 21, 26}, 60] (* Harvey P. Dale, Jul 26 2022 *)

Prog

(PARI) {a(n) = (n%2*7 + 3*n^2) \ 14 * 2 - n%2}
(PARI) {a(n) = (3*n^2 - [0, 10, 12, 6, 6, 12, 10][n%7 + 1]) / 7}
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((x^8-2*x^7-2*x^6-2*x^3-2*x^2+x)/(x^9-2*x^8+x^7-x^2+2*x-1))); // G. C. Greubel, Aug 08 2018

Crossrefs

Cf. A059710.

Sequence in context: A310171 A082643 A310172 * A135524 A083853 A310173

Adjacent sequences: A227846 A227847 A227848 * A227850 A227851 A227852

Keyword

sign

Author

Michael Somos, Oct 31 2013

Status

approved