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

0,2

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).

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

Example

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.

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 *)

Prog

(PARI) {a(n) = if(n, 13*2^(n-1)-6, 0)} \\ Max Alekseyev, May 12 2005
(Magma) [0] cat [13*2^(n-1)-6: n in [1..40]]; // Vincenzo Librandi, May 29 2016
(SageMath) [(13*2^n - 12 - int(n==0))/2 for n in range(41)] # G. C. Greubel, Apr 02 2024

Crossrefs

Cf. A046902.

Sequence in context: A232599 A011934 A159222 * A298288 A299384 A007044

Adjacent sequences: A100203 A100204 A100205 * A100207 A100208 A100209

Keyword

nonn,easy

Author

Jorge Coveiro, Dec 28 2004

Extensions

More terms from Max Alekseyev, May 12 2005

Status

approved