

A056640


At stage 1, start with a unit square. At each successive stage add 4*(n1) new squares around outside with edgetoedge contacts. Sequence gives number of squares (regardless of size) at nth stage.


5



1, 5, 18, 42, 83, 143, 228, 340, 485, 665, 886, 1150, 1463, 1827, 2248, 2728, 3273, 3885, 4570, 5330, 6171, 7095, 8108, 9212, 10413, 11713, 13118, 14630, 16255, 17995, 19856, 21840, 23953, 26197, 28578, 31098, 33763, 36575, 39540, 42660, 45941, 49385, 52998
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OFFSET

1,2


COMMENTS

Number of unit squares at nth stage = n^2 + (n1)^2 (A001844).
First differences are in A255840.  Wesley Ivan Hurt, Mar 13 2015


REFERENCES

Anthony Gardiner, "Mathematical Puzzling," Dover Publications, Inc., Mineola, NY., 1987, page 88.


LINKS

Table of n, a(n) for n=1..43.
Index entries for linear recurrences with constant coefficients, signature (3,2,2,3,1).


FORMULA

G.f.: x(5x^2+2x+1)/((1x^2)(1x)^3).
a(n) = (8*n^32*n+33*(1)^n)/12.  Luce ETIENNE, Aug 21 2014
a(n) = 3*a(n1)2*a(n2)2*a(n3)+3*a(n4)a(n5).  Colin Barker, Sep 29 2014
G.f.: x*(5*x^2+2*x+1) / ((x1)^4*(x+1)).  Colin Barker, Sep 29 2014


MAPLE

A056640:=n>(8*n^32*n+33*(1)^n)/12: seq(A056640(n), n=1..50);


MATHEMATICA

Table[(8*n^3  2*n + 3  3*(1)^n)/12, {n, 30}] (* Wesley Ivan Hurt, Mar 13 2015 *)


PROG

(PARI) Vec(x*(5*x^2+2*x+1)/((x1)^4*(x+1)) + O(x^100)) \\ Colin Barker, Sep 29 2014


CROSSREFS

Cf. A255840.
Sequence in context: A352368 A000338 A212343 * A272703 A272736 A273532
Adjacent sequences: A056637 A056638 A056639 * A056641 A056642 A056643


KEYWORD

nonn,easy


AUTHOR

Robert G. Wilson v, Aug 21 2000


EXTENSIONS

More terms from Colin Barker, Sep 29 2014


STATUS

approved



