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A017569
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a(n) = 12*n + 4.
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14
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4, 16, 28, 40, 52, 64, 76, 88, 100, 112, 124, 136, 148, 160, 172, 184, 196, 208, 220, 232, 244, 256, 268, 280, 292, 304, 316, 328, 340, 352, 364, 376, 388, 400, 412, 424, 436, 448, 460, 472, 484, 496, 508, 520, 532, 544, 556, 568, 580, 592, 604, 616, 628
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OFFSET
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0,1
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COMMENTS
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Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 46 ).
Number of 6 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by 2^m+2m(n-1). Cf. m=2: A008574; m=3: A016933; m=4: A022144; m=5: A017293. - Sergey Kitaev, Nov 13 2004
Except for 4, exponents e such that x^e-x^2+1 is reducible.
If Y and Z are 2-blocks of a (3n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Oct 28 2007
Terms are perfect squares iff n is a generalized octagonal number (A001082), then n = k*(3*k-2) and a(n) = (2*(3k-1))^2. - Bernard Schott, Feb 26 2023
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LINKS
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FORMULA
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Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/36 + log(2)/12. - Amiram Eldar, Dec 12 2021
O.g.f.: 4*(1 + 2*x)/(1 - x)^2.
E.g.f.: 4*exp(x)*(1 + 3*x). (End)
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MATHEMATICA
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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