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

0,2

Comments

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

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).

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)

Example

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).

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 *)

Prog

(Sage) [1]+[2^n + n-1 for n in (1..30)] # G. C. Greubel, Feb 14 2021
(Magma) [1] cat [2^n + n-1: n in [1..30]]; // G. C. Greubel, Feb 14 2021

Crossrefs

Cf. A132735.

Sequence in context: A249557 A061705 A052944 * A263366 A068035 A304973

Adjacent sequences: A132733 A132734 A132735 * A132737 A132738 A132739

Keyword

nonn

Author

Gary W. Adamson, Aug 26 2007

Extensions

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

Status

approved