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A299102
Number of (n + 1, n + 2)-core partitions with odd parts and corresponding order ideals confined to the three outermost diagonals of P_{n + 1, n + 2}.
2
1, 2, 4, 7, 17, 31, 76, 144, 344, 670, 1560, 3103, 7079, 14315, 32152, 65861, 146183, 302456, 665300, 1387172, 3030464, 6356068, 13813464, 29103412, 62999146, 133190358, 287443371, 609299853, 1311936956, 2786508393, 5989399832
OFFSET
0,2
LINKS
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, 7, -6, -15, 11, 12, -6, -5, 1, 1).
FORMULA
G.f.: -(x^9+x^8-4*x^7-6*x^6+8*x^5+9*x^4-5*x^3-5*x^2+x+1)/((x^9+2*x^8-3*x^7-9*x^6+3*x^5+14*x^4-x^3-7*x^2+1)*(x-1)) (proved).
MAPLE
f:= gfun:-rectoproc({-a(n)-2*a(n+1)+3*a(n+2)+9*a(n+3)-3*a(n+4)-14*a(n+5)+a(n+6)+7*a(n+7)-a(n+9)+1, a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 7, a(4) = 17, a(5) = 31, a(6) = 76, a(7) = 144, a(8) = 344, a(9) = 670}, a(n), remember):
map(f, [$0..100]); # Robert Israel, Feb 16 2018
MATHEMATICA
LinearRecurrence[{1, 7, -6, -15, 11, 12, -6, -5, 1, 1}, {1, 2, 4, 7, 17, 31, 76, 144, 344, 670}, 40] (* Jean-François Alcover, Feb 20 2018 *)
CROSSREFS
Cf. A299099.
Sequence in context: A348449 A026775 A299294 * A027238 A299293 A342538
KEYWORD
nonn,easy
AUTHOR
Anthony Zaleski, Feb 16 2018
STATUS
approved