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A244082 a(n) = 32*n^2. 2
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

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Last modified March 3 03:03 EST 2021. Contains 341756 sequences. (Running on oeis4.)