A299099 Number of (n + 1, n + 2)-core partitions with odd parts and corresponding order ideals confined to the two outermost diagonals of P_{n + 1, n + 2}.

1, 2, 4, 7, 15, 27, 56, 104, 210, 398, 791, 1517, 2988, 5769, 11306, 21911, 42820, 83160, 162261, 315496, 615050, 1196676, 2331733, 4538426, 8840719, 17210905, 33521153, 65265737, 127105093, 247489812, 481963369

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, 3, -2, -1, 1).

Formula

G.f.: -(x^4-x^3-x^2+x+1)/(x^5-x^4-2*x^3+3*x^2+x-1).

Mathematica

LinearRecurrence[{1, 3, -2, -1, 1}, {1, 2, 4, 7, 15}, 40] (* Jean-François Alcover, Feb 20 2018 *)

Crossrefs

Cf. A299102.

Sequence in context: A264292 A259592 A291220 * A248574 A136336 A244456

Adjacent sequences: A299096 A299097 A299098 * A299100 A299101 A299102

Keyword

nonn,easy

Author

Anthony Zaleski, Feb 15 2018

Status

approved