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 A308025 a(n) = n*(2*n - 3 - (-1)^n)*(5*n - 2 + (-1)^n)/16. 1
 0, 0, 9, 19, 55, 87, 168, 234, 378, 490, 715, 885, 1209, 1449, 1890, 2212, 2788, 3204, 3933, 4455, 5355, 5995, 7084, 7854, 9150, 10062, 11583, 12649, 14413, 15645, 17670, 19080, 21384, 22984, 25585, 27387, 30303, 32319, 35568, 37810, 41410, 43890, 47859 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Consider the rectangular prisms with dimensions s X t X t, where n = s + t and s < t. Then a(n) is the sum of the areas of the squares that rest on a given space diagonal in each of the rectangular prisms. Sum of the squares of the smaller parts and twice the sum of the squares of the larger parts in the partitions of n into two distinct parts. 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^2 + 2*(n-i)^2. 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). G.f.: x^3*(9 + 10*x + 9*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3). - Colin Barker, May 17 2019 MATHEMATICA Table[n*(2 n - 3 - (-1)^n)*(5 n - 2 + (-1)^n)/16, {n, 60}] PROG (PARI) concat([0, 0], Vec(x^3*(9 + 10*x + 9*x^2 + 2*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, May 17 2019 CROSSREFS Cf. A294286. Sequence in context: A048696 A046103 A146459 * A041158 A146080 A334640 Adjacent sequences:  A308022 A308023 A308024 * A308026 A308027 A308028 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, May 09 2019 STATUS approved

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Last modified July 28 03:49 EDT 2021. Contains 346316 sequences. (Running on oeis4.)