

A058195


Areas of a sequence of rightangled figures described below.


1



1, 7, 23, 57, 118, 218, 370, 590, 895, 1305, 1841, 2527, 3388, 4452, 5748, 7308, 9165, 11355, 13915, 16885, 20306, 24222, 28678, 33722, 39403, 45773, 52885, 60795, 69560, 79240, 89896, 101592, 114393, 128367, 143583, 160113, 178030, 197410, 218330, 240870
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OFFSET

1,2


COMMENTS

From the NW corner to the SE corner, going the upper (or right) way, the edges have lengths n, n1, ..., 2, 1, 1, 2, ..., n1, n. Going the lower (or left) way, the edges have lengths n,1,n1,2,...,2,n1,1,n.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,5,0,5,4,1).


FORMULA

a(n) = [(2n^4+10n^3+13n^2+2n)/24], where [] denotes floor. (For even n there is no need for truncation. For odd n the [] removes 1/8.) A formula without [] is (4n^4+20n^3+26n^2+4n+3+3(1)^(n+1))/48.
From Colin Barker, Oct 07 2015: (Start)
a(n) = 4*a(n1)5*a(n2)+5*a(n4)4*a(n5)+a(n6) for n>6.
a(n) = (2*n^4+10*n^3+13*n^2+2*n)/24 for n even.
a(n) = (2*n^4+10*n^3+13*n^2+2*n3)/24 for n odd.
G.f.: x*(3*x+1) / ((x1)^5*(x+1)).
(End)


EXAMPLE

For n=6 the figure is (assuming the "#" character is square ...):
######
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######
######
######
##########
.#########
.#########
.###########
.############
.############
...#############
...#############
...#############
...#############
......###############
......###############
......###############
..........###########
..........###########
...............######


PROG

(PARI) Vec(x*(3*x+1)/((x1)^5*(x+1)) + O(x^100)) \\ Colin Barker, Oct 07 2015


CROSSREFS

Sequence in context: A027116 A151718 A027918 * A213770 A235683 A037165
Adjacent sequences: A058192 A058193 A058194 * A058196 A058197 A058198


KEYWORD

easy,nonn


AUTHOR

Jonas Wallgren, Nov 26 2000


EXTENSIONS

More terms from James A. Sellers, Dec 06 2000


STATUS

approved



