OFFSET
0,3
COMMENTS
Take an n X n square grid and add unit squares along each side except for the corners --> do this repeatedly along each side with the same restriction until no squares can be added. a(n) is the total area of each figure. The perimeter, P, of each figure is given by P(n) = 4*A042963(n), n>0 (see example).
For n>0, partial sums of a(n) are in A056640.
LINKS
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
G.f.: x*(1+2*x+5*x^2)/((1+x)*(1-x)^3).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
a(n) - a(n-1) = A047471(n). - Wesley Ivan Hurt, Apr 28 2017
EXAMPLE
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n=1 n=2 n=3 n=4 n=5
MATHEMATICA
CoefficientList[Series[x (1 + 2 x + 5 x^2)/((1 + x) (1 - x)^3), {x, 0, 50}], x]
PROG
(Magma) [(4*n^2 - 4*n + 1 - (-1)^n)/2 : n in [0..100]];
(PARI) vector(100, n, (4*(n-1)^2 - 4*(n-1) + 1 + (-1)^n)/2) \\ Derek Orr, Mar 09 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Mar 07 2015
STATUS
approved