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.

1, 3, 7, 13, 23, 41, 75, 141, 271, 529, 1043, 2069, 4119, 8217, 16411, 32797, 65567, 131105, 262179, 524325, 1048615, 2097193, 4194347, 8388653, 16777263, 33554481, 67108915, 134217781, 268435511, 536870969, 1073741883, 2147483709

Offset: 1

Author

Amarnath Murthy, Mar 25 2003

Keywords

• nonn

Examples

			The triangle pertaining to n = 4 is obtained from the solid triangle
        1
      1   1
    1   2   1
  1   3   3   1
giving
        1
      1   1
    1       1
  1   3   3   1
and the sum of all the numbers is 13, so a(4) = 13.
		

Crossrefs

Cf. A081495, A081496, A081497.

First differences of A290707.

Programs

Maple

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

Formula

For n > 1, a(n) = A061761(n-1). - David Wasserman, Jun 03 2004

Extensions

Corrected and extended by David Wasserman, Jun 03 2004