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#94 by Michael De Vlieger at Wed Apr 19 09:04:10 EDT 2023
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#93 by Michel Marcus at Wed Apr 19 01:19:51 EDT 2023
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#92 by G. C. Greubel at Tue Apr 18 23:54:43 EDT 2023
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#91 by G. C. Greubel at Tue Apr 18 23:54:31 EDT 2023
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| FORMULA
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a(n) = floor( (2*n+3)*(n+1)/3 ). Or, a(n) = (2*n+3)*(n+1)/3 but subtract 1/3 if n == 1 mod 3. - N. J. A. Sloane, May 05 2010.
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| MATHEMATICA
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f[x_, y_] := _]:= Floor[ [Abs[ [y/x - -x/y]]; Table[ [f[3, 2 n2n^2 + +n + +2], {n, , 53}] (* Robert G. Wilson v, Aug 11 2010 *)
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| PROG
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(Magma) [Floor(Binomial(2*n+3, 2)/3): n in [0..60]]; // G. C. Greubel, Apr 18 2023
(SageMath) [(binomial(2*n+3, 2)//3) for n in range(61)] # G. C. Greubel, Apr 18 2023
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| STATUS
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approved
editing
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#90 by Michael De Vlieger at Wed Apr 05 18:51:14 EDT 2023
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#89 by Michel Marcus at Wed Apr 05 17:13:43 EDT 2023
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#88 by Stefano Spezia at Wed Apr 05 16:11:33 EDT 2023
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#87 by Stefano Spezia at Wed Apr 05 15:52:27 EDT 2023
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| NAME
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Expansion of ( g.f. (1+ + x+ + 2*x^2)/((1- - x)^2*(1- - x^3)).
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#86 by Stefano Spezia at Wed Apr 05 14:12:59 EDT 2023
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| LINKS
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David Applegate, Omar E. Pol , and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]
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#85 by Stefano Spezia at Wed Apr 05 14:12:08 EDT 2023
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