A008740 Molien series for 3-dimensional group [2+,n] = 2*(n/2).

1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 19, 22, 25, 28, 32, 36, 40, 44, 49, 54, 59, 64, 69, 75, 81, 87, 93, 100, 107, 114, 121, 128, 136, 144, 152, 160, 169, 178, 187, 196, 205, 215, 225, 235, 245, 256, 267, 278, 289, 300, 312, 324, 336, 348, 361, 374, 387, 400, 413, 427, 441, 455, 469, 484

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).

Programs

GAP

List([0..70], n-> Int(((n+3)^2+3)/9)); # G. C. Greubel, Aug 03 2019

Magma

[Floor((n+3)^2+3)/9: n in [0..70]]; // G. C. Greubel, Aug 03 2019

Mathematica

CoefficientList[Series[(1+x^5)/((1-x)^2(1-x^9)),{x,0,70}],x] (* Harvey P. Dale, Aug 27 2011 *)
Floor[((Range[0,70]+3)^2 + 3)/9] (* G. C. Greubel, Aug 03 2019 *)

PARI

vector(70, n, n--; ((n+3)^2+3)\9) \\ G. C. Greubel, Aug 03 2019

Sage

[floor((n+3)^2+3)/9 for n in (0..70)] # G. C. Greubel, Aug 03 2019

Formula

G.f.: (1+x^5)/((1-x)^2*(1-x^9)).

Nearest integer to (n+3)^2/9. [Corrected by Gerald Hillier, Dec 24 2017]

a(n) = a(n-4) + n. - Paul Barry, Jul 14 2004

a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).

a(n) = floor((n^2 + 6*n + 12)/9). - Tani Akinari, Aug 19 2013