A086652 -id:A086652 - cp's OEIS frontend

A086221 Bisection of A086652.

13, 58, 244, 1000, 4048, 16288, 65344, 261760, 1047808, 4192768, 16774144, 67102720, 268423168, 1073717248, 4294918144, 17179770880, 68719280128, 274877513728, 1099510841344, 4398044938240, 17592182898688, 70368737886208

Offset: 1

Marco Matosic, Jul 27 2003

(a(n)-2^(n-1))/2 = A006516(n+1).

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A006516, A086652.

Table[2^(2n+2)-3*2^(n-1),{n,30}] (* or *) nxt[{n_,a_}]:={n+1,4a+3*2^n}; NestList[nxt,{1,13},30][[All,2]] (* Harvey P. Dale, Nov 15 2021 *)

a(n) = 2^(2n+2)-3*2^(n-1).

a(n+1) = 4*a(n)+3*2^n.

Edited and extended by David Wasserman, Feb 17 2005

A384186 Number of permutations of 1, 2,..., n with exactly one rising or falling successon, namely (n-1)n or n(n-1).

Original entry on oeis.org

0, 2, 2, 2, 6, 34, 214, 1506, 11990, 107234, 1065846, 11659426, 139217494, 1801784610, 25124797046, 375531165794, 5989287277014, 101524201538146, 1822662037112950, 34548339122512674, 689469487015534166, 14450128299126915746

Offset: 1

Wolfdieter Lang, May 21 2025

For the number of permutations of length n with exactly one rising or falling successon see A086852. For the number of such permutations without either (n-1)n or n(n-1) see A383857, for n >= 1.

			a(2) = 2*1 from 12 and the reverted 21.
a(3) = 2*1 from 132 and 231.
a(4) = 2*1 from 1342 and 2431.
a(5) = 2*3 from 24513, 24531, 31452 and 31542, 13542, 25413.

Cf. A002464, A086652, A383857.

a(n) = A086652(n) - A383857(n), for n >= 1.
a(n) = a(n-2) + 2*(n-2)*A002464(n-2) + 2*A383857(n-2), for n >= 3, with a(1) = 0 and a(2) = 2. One could also use this recurrence for n >= 2, using a(0) = -2 and a(1) = 0.
a(n) = a(n-2) + 2*(b(n-1) + b(n-2)), with b = A002464, for n >= 3, with a(1) = 0 and a(2) = 2.

cp's OEIS Frontend

A086221 Bisection of A086652.

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