A133124 A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].

1, 3, 7, 16, 35, 74, 153, 312, 631, 1270, 2549, 5108, 10227, 20466, 40945, 81904, 163823, 327662, 655341, 1310700, 2621419, 5242858, 10485737, 20971496, 41943015, 83886054, 167772133, 335544292, 671088611, 1342177250, 2684354529, 5368709088, 10737418207, 21474836446

Offset: 0

Author

Gary W. Adamson, Sep 19 2007

Keywords

• nonn
• easy

Examples

			a(3) = (1, 3, 3, 1) dot (1, 2, 2, 3) = (1 + 6 + 6 + 3).
a(5) = 74 = 2^6 + 2^4 - 6 = 64 + 16 - 6.
		

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. A000079, A133938.

Programs

Magma

[1] cat [5*2^(n - 1) - n -1: n in [1..50]]; // G. C. Greubel, Oct 21 2017

Mathematica

Join[{1}, Table[5*2^(n-1) - n -1, {n,1,50}]] (* G. C. Greubel, Oct 21 2017 *)
LinearRecurrence[{4,-5,2},{1,3,7,16},40] (* Harvey P. Dale, Jun 18 2024 *)

PARI

concat(1, for(n=1,50, print1(5*2^(n - 1) - n - 1, ", "))) \\ G. C. Greubel, Oct 21 2017

Formula

Binomial transform of [1, 2, 2, 3, 2, 3, 2, 3, 2, ...].

a(n) = 5*2^(n-1) - (n+1), for n >= 1.

Row sums of triangle A133938. - Gary W. Adamson, Sep 29 2007

G.f.: 1 + x*(3-5*x+3*x^2)/((1-2*x)*(1-x)^2). - R. J. Mathar, Nov 14 2007

E.g.f.: (5*exp(2*x) - 2*(1+x)*exp(x) - 1)/2. - G. C. Greubel, Oct 21 2017

Extensions

Terms a(9) onward added by G. C. Greubel, Oct 21 2017