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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,base,easy
AUTHOR
Gil Broussard, Feb 18 2016
STATUS
approved

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Last modified May 21 05:34 EDT 2024. Contains 372728 sequences. (Running on oeis4.)