A100206 Row sums of Clark's triangle A046902.

0, 7, 20, 46, 98, 202, 410, 826, 1658, 3322, 6650, 13306, 26618, 53242, 106490, 212986, 425978, 851962, 1703930, 3407866, 6815738, 13631482, 27262970, 54525946, 109051898, 218103802, 436207610, 872415226, 1744830458, 3489660922

Offset: 0

Author

Jorge Coveiro, Dec 28 2004

Keywords

• nonn
• easy

Examples

			a(0) =  0.
a(1) =  6 +  1.
a(2) = 12 +  7 +  1.
a(3) = 18 + 19 +  8 + 1.
a(4) = 24 + 37 + 27 + 9 + 1.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Clark's Triangle.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A046902.

Programs

Magma

[0] cat [13*2^(n-1)-6: n in [1..40]]; // Vincenzo Librandi, May 29 2016

Mathematica

Join[{0}, Table[13 2^(n-1) - 6, {n, 1, 40}]] (* Vincenzo Librandi, May 29 2016 *)
LinearRecurrence[{3,-2},{0,7,20},30] (* Harvey P. Dale, Jul 07 2024 *)

PARI

{a(n) = if(n,13*2^(n-1)-6,0)} \\ Max Alekseyev, May 12 2005

SageMath

[(13*2^n - 12 - int(n==0))/2 for n in range(41)] # G. C. Greubel, Apr 02 2024

Formula

a(0)=0; for n>0, a(n) = 13*2^(n-1) - 6. - Max Alekseyev, May 12 2005

From Chai Wah Wu, May 28 2016: (Start)

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

G.f.: x*(7 - x)/((1 - x )*(1 - 2*x)). (End)

E.g.f.: (1/2)*(13*exp(2*x) - 12*exp(x) - 1). - G. C. Greubel, Apr 02 2024

Extensions

More terms from Max Alekseyev, May 12 2005