A080522 Leading diagonal of triangle in A080521.

1, 3, 5, 10, 22, 49, 107, 228, 476, 979, 1993, 4030, 8114, 16293, 32663, 65416, 130936, 261991, 524117, 1048386, 2096942, 4194073, 8388355, 16776940, 33554132, 67108539, 134217377, 268435078, 536870506, 1073741389, 2147483183

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

a(n) = 2^n-(n-1)*(n-2)/2-n+1 for n>1. - Lambert Herrgesell (zero815(AT)googlemail.com), Mar 14 2006

a(n) = A014844(n), n>1. - R. J. Mathar, Sep 19 2008

From Colin Barker, Dec 18 2012: (Start)

a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4) for n>5.

G.f.: -x*(2*x^4-5*x^3+x^2+2*x-1) / ((x-1)^3*(2*x-1)). (End)

Mathematica

Join[{1}, Array[2^# - #*(# - 1)/2 &, 50, 2]] (* Paolo Xausa, Mar 16 2024 *)

Prog

(Magma) [1] cat[2^n-(n-1)*(n-2)/2-n+1: n in [2..40]]; // Vincenzo Librandi, Apr 18 2012

Crossrefs

Cf. A080521.

Sequence in context: A053709 A102772 A018005 * A173232 A132332 A209001

Adjacent sequences: A080519 A080520 A080521 * A080523 A080524 A080525

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 21 2003

Extensions

More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Mar 14 2006

Status

approved