A132736 Row sums of triangle A132735.

1, 2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, 2058, 4107, 8204, 16397, 32782, 65551, 131088, 262161, 524306, 1048595, 2097172, 4194325, 8388630, 16777239, 33554456, 67108889, 134217754, 268435483, 536870940, 1073741853, 2147483678

Offset: 0

Author

Gary W. Adamson, Aug 26 2007

Keywords

• nonn

Comments

Apart from first term, the same as A052944. - R. J. Mathar, Jun 12 2008

Examples

			a(4) = 19 = sum of row 4 terms of triangle A132735: (1 + 5 + 7 + 5 + 1).
a(3) = 10 = (1, 3, 3, 1) dot (1, 1, 2, 0) = (1 + 3 + 6 + 0).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A132735.

Programs

Magma

[1] cat [2^n + n-1: n in [1..30]]; // G. C. Greubel, Feb 14 2021

Maple

a:= proc(n) option remember; if n=0 then 1 else add((binomial(n,j)+1), j=0..n-1) fi end: seq(a(n), n=0..31);# Zerinvary Lajos, Mar 29 2009

Mathematica

Table[2^n + n-1 + Boole[n==0], {n,0,30}] (* G. C. Greubel, Feb 14 2021 *)

Sage

[1]+[2^n + n-1 for n in (1..30)] # G. C. Greubel, Feb 14 2021

Formula

Binomial transform of [1, 1, 2, 0, 2, 0, 2, 0, 2, ...].

From Colin Barker, Aug 12 2012: (Start)

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

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

From G. C. Greubel, Feb 14 2021: (Start)

a(n) = 2^n + n - 1 + [n=0].

E.g.f.: 1 - (1-x)*exp(x) + exp(2*x). (End)

Extensions

More terms from R. J. Mathar, Jun 12 2008