A192447 a(n) = n*(n-1)/2 if this is even, otherwise (n*(n-1)/2) + 1.
0, 2, 4, 6, 10, 16, 22, 28, 36, 46, 56, 66, 78, 92, 106, 120, 136, 154, 172, 190, 210, 232, 254, 276, 300, 326, 352, 378, 406, 436, 466, 496, 528, 562, 596, 630, 666, 704, 742, 780, 820, 862, 904, 946, 990, 1036, 1082, 1128, 1176, 1226, 1276, 1326, 1378, 1432
Offset: 1
Examples
a(3) = 4: Let the initial state be Aa, Bb, Cc. Swap(AB) to get Ab, Ba, Cc. Swap(AC) to get Ac, Ba, Cb. Swap(BC) to get Ac, Bb, Ca. Swap(AC) to get Aa, Bb, Cc, done.
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).
Crossrefs
Programs
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Mathematica
Table[(n^2 - n + 1 - (-1)^(n (n - 1)/2))/2, {n, 1, 60}] (* Bruno Berselli, Jun 07 2019 *) LinearRecurrence[{3,-4,4,-3,1}, {0,2,4,6,10}, 54] (* Georg Fischer, Oct 26 2020 *) -
PARI
a(n) = my(m=n*(n-1)/2); if (m % 2, m+1, m); \\ Michel Marcus, Jun 07 2019
Formula
a(n) = n*(n-1)/2 if this is even and a(n) = (n*(n-1)/2) + 1 otherwise.
a(n) = 2*A054925(n).
G.f.: 2*x*(x^2 - x + 1)/((1 - x)^3*(1 + x^2)).
a(n) = (n^2 - n + 1 - (-1)^(n*(n-1)/2))/2. - Guenther Schrack, Jun 04 2019
Sum_{n>=2} 1/a(n) = 2 - Pi/2 + Pi*sinh(sqrt(7)*Pi/4)/(sqrt(7)*(1/sqrt(2) + cosh(sqrt(7)*Pi/4))). - Amiram Eldar, Dec 14 2024
Comments