login
A298367
Number of (n + 1, n + 2)-core partitions with each part repeated at most four times.
0
1, 2, 5, 14, 42, 90, 213, 527, 1326, 3317, 8022, 19608, 48272, 119073, 293109, 719074, 1766201, 4342666, 10679582, 26253546, 64516501, 158569355, 389788182, 958172417, 2355231458, 5789058028, 14229546200, 34976963777, 85975197161, 211329783890, 519453451997
OFFSET
0,2
FORMULA
G.f.: -(14*x^4+5*x^3+2*x^2+x+1)/(14*x^5+5*x^4+2*x^3+x^2+x-1).
MATHEMATICA
LinearRecurrence[{1, 1, 2, 5, 14}, {1, 2, 5, 14, 42}, 40] (* Jean-François Alcover, Feb 20 2018 *)
CoefficientList[ Series[-(14x^4 + 5x^3 + 2x^2 + x + 1)/(14x^5 + 5x^4 + 2x^3 + x^2 + x - 1), {x, 0, 33}], x] (* Robert G. Wilson v, Feb 24 2018 *)
PROG
(PARI) x='x+O('x^99); Vec((1+x+2*x^2+5*x^3+14*x^4)/(1-x-x^2-2*x^3-5*x^4-14*x^5)) \\ Altug Alkan, Mar 03 2018
CROSSREFS
Sequence in context: A148325 A281594 A174176 * A025274 A132833 A293347
KEYWORD
nonn,easy
AUTHOR
Anthony Zaleski, Feb 15 2018
STATUS
approved