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 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 (list; graph; refs; listen; history; text; internal format)
 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 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(k-1,2)*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(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) 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

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Last modified June 19 15:03 EDT 2021. Contains 345141 sequences. (Running on oeis4.)