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

Author

Gil Broussard, Feb 18 2016

Keywords

• nonn
• base
• easy

Examples

			     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
		

Links

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

Programs

Magma

[1] cat [2*(2^n-1)+(n-2)*(2^(n-1)+1): n in [2..40]]; // Vincenzo Librandi, Feb 27 2016

Mathematica

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

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