A125176 Row sums of A125175.

1, 3, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

a(1) = 1, a(2) = 3, a(n) = 7*2^(n-3) for n>=3.

From Colin Barker, Oct 12 2013: (Start)

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

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

E.g.f.: (7*exp(2*x) - 7 - 6*x - 2*x^2)/8. - G. C. Greubel, Jun 05 2019

Example

First few rows of A125175 are:
  1;
  1, 2;
  1, 3, 3;
  1, 4, 5, 4;
  ....
a(4) = 1 + 4 + 5 + 4 = 14.
a(6) = 1 + 6 + 14 + 20 + 9 + 6 = 56 = 7*8 = 7*2^3.

Mathematica

Rest@CoefficientList[Series[x*(1+x+x^2)/(1-2*x), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 12 2013 *)

Prog

(PARI) concat([1, 3], vector(30, n, 7*2^(n-1))) \\ G. C. Greubel, Jun 05 2019
(Magma) [1, 3] cat [7*2^(n-3): n in [3..40]];  // G. C. Greubel, Jun 05 2019
(Sage) [1, 3]+[7*2^(n-3) for n in (3..40)] # G. C. Greubel, Jun 05 2019
(GAP) Concatenation([1, 3], List([3..40], n-> 7*2^(n-3))) # G. C. Greubel, Jun 05 2019
(Python) print([7*2**n//8 for n in range(1, 50)]) # Karl V. Keller, Jr., May 11 2022

Crossrefs

Cf. A125175.

Essentially identical to A005009.

Sequence in context: A140741 A088209 A089074 * A153234 A293334 A266625

Adjacent sequences: A125173 A125174 A125175 * A125177 A125178 A125179

Keyword

nonn,easy

Author

Gary W. Adamson, Nov 22 2006

Extensions

More terms from N. J. A. Sloane, Dec 15 2007

Status

approved