|
| |
| |
|
|
|
0, 32, 128, 288, 512, 800, 1152, 1568, 2048, 2592, 3200, 3872, 4608, 5408, 6272, 7200, 8192, 9248, 10368, 11552, 12800, 14112, 15488, 16928, 18432, 20000, 21632, 23328, 25088, 26912, 28800, 30752, 32768, 34848, 36992, 39200, 41472, 43808, 46208, 48672, 51200
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
Geometric connections of a(n) to the area and perimeter of a square.
Area:
. half the area of a square with side 8n (cf. A008590);
. area of a square with diagonal 8n (cf. A008590);
. twice the area of a square with side 4n (cf. A008586);
. four times the area of a square with diagonal 4n (cf. A008586);
. eight times the area of a square with side 2n (cf. A005843);
. sixteen times the area of a square with diagonal 2n (cf. A005843);
. thirty two times the area of a square with side n (cf. A001477);
. sixty four times the area of a square with diagonal n (cf. A001477).
Perimeter:
. perimeter of a square with side 8n^2 (cf. A139098);
. twice the perimeter of a square with side 4n^2 (cf. A016742);
. four times the perimeter of a square with side 2n^2 (cf. A001105);
. eight times the perimeter of a square with side n^2 (cf. A000290).
Sequence found by reading the line from 0, in the direction 0, 32, ..., in the square spiral whose vertices are the generalized 18-gonal numbers. - Omar E. Pol, May 10 2018
|
|
|
LINKS
|
Table of n, a(n) for n=0..40.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
G.f.: 32*x*(1+x)/(1-x)^3.
a(n) = 2 * A016802(n).
a(n) = 4 * A139098(n).
a(n) = 8 * A016742(n).
a(n) = 16 * A001105(n).
a(n) = 32 * A000290(n).
a(n) = A010021(n)-2 for n>0. - Bruno Berselli, Jun 24 2014
|
|
|
MAPLE
|
A244082:=n->32*n^2; seq(A244082(n), n=0..50);
|
|
|
MATHEMATICA
|
32 Range[0, 50]^2 (* or *)
Table[32 n^2, {n, 0, 50}] (* or *)
CoefficientList[Series[32 x (1 + x)/(1 - x)^3, {x, 0, 30}], x]
|
|
|
PROG
|
(MAGMA) [32*n^2 : n in [0..50]];
(PARI) a(n)=32*n^2 \\ Charles R Greathouse IV, Jun 17 2017
|
|
|
CROSSREFS
|
Cf. A000290, A001105, A010021, A016742, A016802, A139098.
Pentasection of A077221, A181900.
Sequence in context: A264480 A247155 A239728 * A033323 A091905 A100626
Adjacent sequences: A244079 A244080 A244081 * A244083 A244084 A244085
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Wesley Ivan Hurt, Jun 19 2014
|
|
|
STATUS
|
approved
|
| |
|
|
