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A244971
Number of regions in the symmetric representation of sigma(n) on the four quadrants.
8
1, 1, 4, 1, 4, 1, 4, 1, 8, 4, 4, 1, 4, 4, 8, 1, 4, 1, 4, 1, 12, 4, 4, 1, 8, 4, 12, 1, 4, 1, 4, 1, 12, 4, 8, 1, 4, 4, 12, 1, 4, 1, 4, 4, 8, 4, 4, 1, 8, 8, 12, 4, 4, 1, 12, 1, 12, 4, 4, 1, 4, 4, 16, 1, 12, 1, 4, 4, 12, 8, 4, 1, 4, 4, 12, 4, 8, 4, 4, 1, 16, 4, 4, 1, 12, 4, 12, 1, 4, 1
OFFSET
1,3
COMMENTS
Partial sums give A244970.
Number of terraces at the n-th level (starting from the top) of the stepped pyramid described in A244050. - Omar E. Pol, Apr 20 2016
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..5000 (computed from the b-file of A237271 provided by Michel Marcus)
FORMULA
a(n) = 1, if A237271(n) = 1.
a(n) = 4*(A237271(n) - 1), if A237271(n) > 1.
EXAMPLE
From Omar E. Pol, Apr 20 2016: (Start)
Illustration of the top view of the stepped pyramid with 16 levels:
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
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. | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
. _ _| | _ _ _ _ _ _ _ _ _ _ _ _ _ _ | |_ _
. _| _ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _ |_
. _| _| _| | _ _ _ _ _ _ _ _ _ _ _ _ | |_ |_ |_
. | _| |_ _| |_ _ _ _ _ _ _ _ _ _ _ _| |_ _| |_ |
. _ _ _| | _ _| | _ _ _ _ _ _ _ _ _ _ | |_ _ | |_ _ _
. | _ _ _|_| | _| |_ _ _ _ _ _ _ _ _ _| |_ | |_|_ _ _ |
. | | | _ _ _| _|_ _| _ _ _ _ _ _ _ _ |_ _|_ |_ _ _ | | |
. | | | | | _ _ _| | _| |_ _ _ _ _ _ _ _| |_ | |_ _ _ | | | | |
. | | | | | | | _ _|_| _| _ _ _ _ _ _ |_ |_|_ _ | | | | | | |
. | | | | | | | | | _ _| |_ _ _ _ _ _| |_ _ | | | | | | | | |
. | | | | | | | | | | | _ _| _ _ _ _ |_ _ | | | | | | | | | | |
. | | | | | | | | | | | | | _|_ _ _ _|_ | | | | | | | | | | | | |
. | | | | | | | | | | | | | | | _ _ | | | | | | | | | | | | | | |
. | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
. | | | | | | | | | | | | | | | |_ _| | | | | | | | | | | | | | | |
. | | | | | | | | | | | | | |_|_ _ _ _|_| | | | | | | | | | | | | |
. | | | | | | | | | | | |_|_ |_ _ _ _| _|_| | | | | | | | | | | |
. | | | | | | | | | |_|_ |_ _ _ _ _ _| _|_| | | | | | | | | |
. | | | | | | | |_|_ _ |_ |_ _ _ _ _ _| _| _ _|_| | | | | | | |
. | | | | | |_|_ _ | |_ |_ _ _ _ _ _ _ _| _| | _ _|_| | | | | |
. | | | |_|_ _ |_|_ _| |_ _ _ _ _ _ _ _| |_ _|_| _ _|_| | | |
. | |_|_ _ _ | |_ |_ _ _ _ _ _ _ _ _ _| _| | _ _ _|_| |
. |_ _ _ | |_|_ | |_ _ _ _ _ _ _ _ _ _| | _|_| | _ _ _|
. | |_ |_ _ |_ _ _ _ _ _ _ _ _ _ _ _| _ _| _| |
. |_ |_ |_ | |_ _ _ _ _ _ _ _ _ _ _ _| | _| _| _|
. |_ |_ _| |_ _ _ _ _ _ _ _ _ _ _ _ _ _| |_ _| _|
. |_ _ | |_ _ _ _ _ _ _ _ _ _ _ _ _ _| | _ _|
. | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
. | |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
. |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
Note that the above diagram contains a hidden pattern, simpler, which emerges from the front view of every corner of the stepped pyramid.
For more information about the hidden pattern see A237593.
(End)
PROG
(PARI) lista() = {v = readvec("b237271.txt"); for (i=1, #v, vi = v[i]; if (vi == 1, w = 1, w = 4*(vi-1)); print1(w, ", "); ); } \\ Michel Marcus, Sep 29 2014
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jul 08 2014
STATUS
approved