Revision History for A260006
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#70 by Harvey P. Dale at Sat Mar 04 11:32:16 EST 2023
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#69 by Harvey P. Dale at Sat Mar 04 11:32:11 EST 2023
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| MATHEMATICA
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LinearRecurrence[{6, -13, 12, -4}, {0, 3, 12, 35}, 40] (* Harvey P. Dale, Mar 04 2023 *)
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| STATUS
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approved
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#68 by Charles R Greathouse IV at Thu Sep 08 08:46:13 EDT 2022
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Discussion
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| Thu Sep 08
| 08:46
| OEIS Server: https://oeis.org/edit/global/2944
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#67 by Joerg Arndt at Fri Dec 31 02:03:16 EST 2021
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#66 by Michel Marcus at Fri Dec 31 00:29:58 EST 2021
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#65 by G. C. Greubel at Fri Dec 31 00:24:09 EST 2021
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#64 by G. C. Greubel at Fri Dec 31 00:23:57 EST 2021
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| COMMENTS
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f(1,n,n) = 2^n(*(n+2) - (n+2) = (2^n- - 1)*(n+2).
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| FORMULA
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a(n) = (2^n- -1)*(n+2).
G.f.: x*(2*x^23 - 6*x + 3) / ((2*x-^2) / ((1-x)^2*(1-2*x-1)^2). - Colin Barker, Jul 29 2015
E.g.f.: (.: 2**(x+21)*exp(2*x) - (x+2)*exp(x). - Robert Israel, Aug 23 2015
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| MATHEMATICA
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Table[(2^n - -1) ()(n + +2), {n, 0, 30}] (* Michael De Vlieger, Aug 22 2015 *)
CoefficientList[Series[x (2 x(3 -6x +2x^2 - 6 x + 3)/((x - 1-x)^2 (2 x - 1-2x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 22 2015 *)
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| PROG
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(PARI) concat(0, Vec(x*(2*x^23-6*x+3)/((2*x-^2)/((1-x)^2*(1-2*x-1)^2) + O(x^40))) \\ Colin Barker, Jul 29 2015
(Sage) [(n+2)*(2^n -1) for n in (0..30)] # G. C. Greubel, Dec 30 2021
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| CROSSREFS
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Cf. A000295 (f(1,0,n)), A000325 (f(1,2,n)), A005408 (f(1,n,1) = 2n+1), A001787 (n*2^(n-1)), A079583 (f(1,1,n)), A123720 (f(1,4,n)), A133124 (f(1,3,n)), A260002, A260003, A260004, A260005.)).
Cf. A260002, A260003, A260004, A260005.
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approved
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#63 by Alois P. Heinz at Tue Nov 16 20:10:25 EST 2021
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#62 by Alois P. Heinz at Tue Nov 16 20:10:22 EST 2021
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| COMMENTS
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a(n-2) is the number of ways we can write [n] as the union of 2 nonempty sets of sizes i, j which intersect in exactly 1 element (1 < i, j < n; i = j allowed), n>=2.
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approved
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#61 by Wolfdieter Lang at Tue Nov 16 15:29:24 EST 2021
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