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 A298992 a(n) = (2*n-3-(-1)^n)*(22*n^2-21*n+5*n*(-1)^n)/96. 1
 0, 0, 5, 12, 35, 58, 112, 160, 258, 340, 495, 620, 845, 1022, 1330, 1568, 1972, 2280, 2793, 3180, 3815, 4290, 5060, 5632, 6550, 7228, 8307, 9100, 10353, 11270, 12710, 13760, 15400, 16592, 18445, 19788, 21867, 23370, 25688, 27360, 29930, 31780, 34615, 36652 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Consider the partitions of n into two distinct parts (p,q) where p < q. Then a(n) is the total area of the family of rectangles (and the areas of the squares on their sides) with dimensions p and |q - p|. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1). FORMULA a(n) = Sum_{i=1..floor((n-1)/2)} i*(n-2*i) + 2*i^2 + 2*(n-2*i)^2. From Colin Barker, Apr 23 2019: (Start) G.f.: x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3). a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7. (End) MATHEMATICA Table[(2 n - 3 - (-1)^n) (22 n^2 - 21 n + 5 n (-1)^n)/96, {n, 50}] PROG (PARI) concat([0, 0], Vec(x^3*(5 + 7*x + 8*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, Apr 23 2019 CROSSREFS Cf. A302647, A302758. Sequence in context: A192243 A292104 A136113 * A050189 A308344 A116995 Adjacent sequences:  A298989 A298990 A298991 * A298993 A298994 A298995 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Apr 16 2018 STATUS approved

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Last modified August 9 12:53 EDT 2022. Contains 356026 sequences. (Running on oeis4.)