A269059 Construct a hollow square of 1's of side n and fill its interior with 0's to create a stack of n binary numbers. Express the sum of the stack in decimal.

1, 6, 19, 48, 113, 258, 579, 1284, 2821, 6150, 13319, 28680, 61449, 131082, 278539, 589836, 1245197, 2621454, 5505039, 11534352, 24117265, 50331666, 104857619, 218103828, 452984853, 939524118, 1946157079, 4026531864, 8321499161, 17179869210, 35433480219, 73014444060

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Index entries for linear recurrences with constant coefficients, signature (6, -13, 12, -4).

Formula

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

G.f.: x*(1-2*x^2)^2/((1-2*x)^2*(1-x)^2). - Robert Israel, Feb 18 2016

Example

     1   1 1  3    1 1 1  7    1 1 1 1  15
a(1)=1   1 1 +3    1 0 1 +5    1 0 0 1 + 9
         a(2)=6    1 1 1 +7    1 0 0 1 + 9
                    a(3)=19    1 1 1 1 +15
                                   a(4)=48

Mathematica

Join[{1}, LinearRecurrence[{6, -13, 12, -4}, {0, 6, 19, 48}, {2, 32}]] (* Jean-François Alcover, Feb 27 2016 *)

Prog

(Magma) [1] cat [2*(2^n-1)+(n-2)*(2^(n-1)+1): n in [2..40]]; // Vincenzo Librandi, Feb 27 2016
(PARI) a(n) = if (n==1, 1, 2*(2^n-1)+(n-2)*(2^(n-1)+1)); \\ Michel Marcus, Mar 24 2016
(PARI) Vec(x*(1-2*x^2)^2/((1-2*x)^2*(1-x)^2) + O(x^100)) \\ Altug Alkan, Mar 24 2016

Crossrefs

Sequence in context: A273079 A073362 A095264 * A324218 A229731 A360951

Adjacent sequences: A269056 A269057 A269058 * A269060 A269061 A269062

Keyword

nonn,base,easy

Author

Gil Broussard, Feb 18 2016

Status

approved