A102543 Antidiagonal sums of the antidiagonals of Losanitsch's triangle.
1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 16, 24, 33, 49, 69, 102, 145, 214, 307, 452, 653, 960, 1393, 2046, 2978, 4371, 6376, 9354, 13665, 20041, 29307, 42972, 62884, 92191, 134974, 197858, 289772, 424746, 622198, 911970, 1336121, 1958319, 2869417, 4205538, 6162579, 9031996, 13235661, 19398240
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- R. J. Mathar, Paving rectangular regions with rectangular tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], 2013, Table 25.
- Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,1,-1,0,-1).
Programs
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Maple
A102543 := proc(n): (A000930(n)+x(n)+x(n-1)+x(n-3))/2 end: A000930:=proc(n): sum(binomial(n-2*i, i), i=0..n/3) end: x:=proc(n): if type(n, even) then A000930(n/2) else 0 fi: end: seq(A102543(n), n=0..38); # Johannes W. Meijer, Jul 14 2011
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Mathematica
CoefficientList[Series[(1 - x^2 - x^4 - x^6)/((x^3 + x - 1)*(x^6 + x^2 - 1)), {x, 0, 50}], x] (* G. C. Greubel, Apr 27 2017 *) LinearRecurrence[{1,1,0,0,-1,1,-1,0,-1},{1,1,1,2,2,3,4,6,8},50] (* Harvey P. Dale, Dec 14 2023 *) -
PARI
x='x+O('x^50); Vec((1 - x^2 - x^4 - x^6)/((x^3 + x - 1)*(x^6 + x^2 - 1))) \\ G. C. Greubel, Apr 27 2017
Formula
a(n) = A068927(n-1), n>3.
From Johannes W. Meijer, Jul 14 2011: (Start)
G.f.: (-1/2)*(1/(x^3+x-1)+(1+x+x^3)/(x^6+x^2-1))= ( 1-x^2-x^4-x^6 ) / ( (x^3+x-1)*(x^6+x^2-1) ).
Comments