A081494 - OEIS

A081494

Start with Pascal's triangle; form a triangle by sliding down n steps from top on both sides and including the horizontal row, deleting the inner numbers; a(n) = sum of entries on perimeter of triangle.

%I #12 Jun 25 2022 21:43:27

%S 1,3,7,13,23,41,75,141,271,529,1043,2069,4119,8217,16411,32797,65567,

%T 131105,262179,524325,1048615,2097193,4194347,8388653,16777263,

%U 33554481,67108915,134217781,268435511,536870969,1073741883,2147483709

%N Start with Pascal's triangle; form a triangle by sliding down n steps from top on both sides and including the horizontal row, deleting the inner numbers; a(n) = sum of entries on perimeter of triangle.

%F For n > 1, a(n) = A061761(n-1). - _David Wasserman_, Jun 03 2004

%e The triangle pertaining to n = 4 is obtained from the solid triangle

%e 1

%e 1 1

%e 1 2 1

%e 1 3 3 1

%e giving

%e 1

%e 1 1

%e 1 3 3 1

%e and the sum of all the numbers is 13, so a(4) = 13.

%p restart:a:= proc(n) option remember; if n=0 then 1 else add((binomial (n,j)+2), j=0..n-1) fi end: seq (a(n), n=0..31); # _Zerinvary Lajos_, Mar 29 2009

%Y Cf. A081495, A081496, A081497.

%Y First differences of A290707.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 25 2003

%E Corrected and extended by _David Wasserman_, Jun 03 2004