OFFSET
1,2
COMMENTS
This is row 21 of a table of values related to Molien series. It is the product of the sequence on row 3 (A008619) with the sequence on row 7 (A001400).
This table may be constructed by moving the rows of table A008284 to prime locations and generating the composite locations by multiplication in a manner similar to the calculation illustrated in the present sequence.
Rows 1 thru 20 and 22 thru 25 are as follows:
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, 0, -1, 2, 2, -1, 0, -3, 1, 2, -1).
FORMULA
G.f.: x/((x^2+x+1)*(x^2+1)*(x+1)^3*(x-1)^6). - Alois P. Heinz, Nov 10 2008
a(n)= -A049347(n)/27 +(2*n+11)*(6*n^4+132*n^3+914*n^2+2068*n+1055)/69120 -(-1)^n*(51/512+n^2/256+11*n/256+A057077(n)/32 ). - R. J. Mathar, Nov 21 2008
MAPLE
a:= proc(n) local m, r; m:= iquo (n, 12, 'r'); r:= r+1; (19+ (145+ (260+ 15* (r+9)*r+ (405+ 90*r+ 216*m) *m) *m) *m) *m/5+ [0, 1, 2, 5, 9, 17, 27, 44, 65, 97, 136, 191][r]+ [0, 16, 37, 77, 128, 208, 307, 447, 616, 840, 1105, 1441][r]*m/2+ [0, 52, 119, 213, 328, 476, 651, 865, 1112, 1404, 1735, 2117][r]*m^2/2 end: seq (a(n), n=1..50); # Alois P. Heinz, Nov 10 2008
MATHEMATICA
CoefficientList[Series[x/((x^2+x+1)(x^2+1)(x+1)^3 (x-1)^6), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, -3, 0, -1, 2, 2, -1, 0, -3, 1, 2, -1}, {0, 1, 2, 5, 9, 17, 27, 44, 65, 97, 136, 191, 257}, 50] (* Harvey P. Dale, Feb 17 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alford Arnold, Apr 29 2008, May 01 2008
EXTENSIONS
More terms from Alois P. Heinz, Nov 10 2008
Corrected A-number in definition. Added formula. - R. J. Mathar, Nov 21 2008
STATUS
approved