|
|
|
|
1, 2, 5, 9, 17, 27, 44, 65, 97, 136, 191, 257, 346, 451, 587, 746, 946, 1177, 1461, 1786, 2178, 2623, 3151, 3746, 4443, 5223, 6126, 7131, 8283, 9558, 11007, 12603, 14403, 16377, 18588, 21003, 23692, 26618, 29858, 33372, 37244, 41430, 46022, 50972
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
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
|
|
|
EXTENSIONS
|
Corrected A-number in definition. Added formula. - R. J. Mathar, Nov 21 2008
|
|
STATUS
|
approved
|
|
|
|