A132730 Row sums of triangle A132729.

1, 2, 3, 8, 21, 50, 111, 236, 489, 998, 2019, 4064, 8157, 16346, 32727, 65492, 131025, 262094, 524235, 1048520, 2097093, 4194242, 8388543, 16777148, 33554361, 67108790, 134217651, 268435376, 536870829

Offset: 0

Author

Gary W. Adamson, Aug 26 2007

Keywords

• nonn
• easy

Examples

			a(4) = 21 = sum of row 4 terms of triangle A132729: (1 + 5 + 9 + 5 + 1).
a(3) = 8 = (1, 3, 3, 1) dot (1, 1, 0, 4) = (1 + 3 + 0 + 4).
		

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. A132729.

Programs

Magma

[1] cat [2^(n+1) -3*n +1: n in [0..30]]; // G. C. Greubel, Feb 14 2021

Mathematica

LinearRecurrence[{4,-5,2},{1,2,3,8},30] (* Harvey P. Dale, Dec 30 2015 *)
Table[2^(n+1) -3*n +1 -2*Boole[n==0], {n,0,30}] (* G. C. Greubel, Feb 14 2021 *)

Sage

[1]+[2^(n+1) -3*n +1 for n in (1..30)] # G. C. Greubel, Feb 14 2021

Formula

Binomial transform of [1, 1, 0, 4, 0, 4, 0, 4, ...].

a(n) = 2^(n+1) - 3*n + 1, for n > 0. - R. J. Mathar, Apr 04 2012

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

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

E.g.f.: -2 + (1-3*x)*exp(x) + 2*exp(2*x). (End)