A298367 Number of (n + 1, n + 2)-core partitions with each part repeated at most four times.

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

Links

Table of n, a(n) for n=0..30.

Anthony Zaleski, Doron Zeilberger, On the Intriguing Problem of Counting (n+1,n+2)-Core Partitions into Odd Parts, arXiv:1712.10072 [math.CO], 2017.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 2, 5, 14).

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

Adjacent sequences: A298364 A298365 A298366 * A298368 A298369 A298370

Keyword

nonn,easy

Author

Anthony Zaleski, Feb 15 2018

Status

approved