

A334694


a(n) = (n/4)*(n^3+2*n^2+5*n+8).


4



0, 4, 17, 51, 124, 260, 489, 847, 1376, 2124, 3145, 4499, 6252, 8476, 11249, 14655, 18784, 23732, 29601, 36499, 44540, 53844, 64537, 76751, 90624, 106300, 123929, 143667, 165676, 190124, 217185, 247039, 279872, 315876, 355249, 398195, 444924, 495652, 550601, 609999, 674080, 743084, 817257, 896851, 982124, 1073340
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OFFSET

0,2


COMMENTS

Consider a figure made up of a row of n >= 1 adjacent congruent rectangles in which all possible diagonals of the rectangles have been drawn. The number of regions formed is A306302. If we distort all these diagonals very slightly so that no three lines meet at a point, the number of regions changes to a(n).


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for sequences related to stained glass windows
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

Satisfies the identity a(n) = A306302(n) + Sum_{k=3..(n+1)} binomial(k1,2)*A333275(n,2*k). E.g. for n=4 we have a(4) = 104 + 8*1 + 2*3 + 1*6 = 124.
From Colin Barker, May 27 2020: (Start)
G.f.: x*(4  3*x + 6*x^2  x^3) / (1  x)^5.
a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5) for n>4.
(End)


PROG

(PARI) concat(0, Vec(x*(4  3*x + 6*x^2  x^3) / (1  x)^5 + O(x^40))) \\ Colin Barker, May 27 2020


CROSSREFS

Cf. A306302, A331452, A333275.
Sequence in context: A173704 A297817 A184445 * A228960 A131339 A047668
Adjacent sequences: A334691 A334692 A334693 * A334695 A334696 A334697


KEYWORD

nonn,easy


AUTHOR

Scott R. Shannon and N. J. A. Sloane, May 19 2020


STATUS

approved



