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A058195 Areas of a sequence of right-angled 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From the NW corner to the SE corner, going the upper (or right) way, the edges have lengths n, n-1, ..., 2, 1, 1, 2, ..., n-1, n. Going the lower (or left) way, the edges have lengths n,1,n-1,2,...,2,n-1,1,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(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6) 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*n-3)/24 for n odd.

G.f.: -x*(3*x+1) / ((x-1)^5*(x+1)).

(End)

EXAMPLE

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

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.#########

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...#############

...#############

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PROG

(PARI) Vec(-x*(3*x+1)/((x-1)^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

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Last modified December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)