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 A323724 a(n) = n*(2*(n - 2)*n + (-1)^n + 3)/4. 5
 0, 0, 2, 6, 20, 40, 78, 126, 200, 288, 410, 550, 732, 936, 1190, 1470, 1808, 2176, 2610, 3078, 3620, 4200, 4862, 5566, 6360, 7200, 8138, 9126, 10220, 11368, 12630, 13950, 15392, 16896, 18530, 20230, 22068, 23976, 26030, 28158, 30440, 32800, 35322, 37926, 40700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n > 1, a(n) is the superdiagonal sum of the matrix M(n) whose permanent is A322277(n). All the terms of this sequence are even numbers (A005843), but do not end with 4. LINKS Stefano Spezia, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1). FORMULA O.g.f.: 2*x^2*(1 + x + 3*x^2 + x^3)/((1 - x)^4*(1 + x)^2). E.g.f.: (1/2)*x*(exp(x)*x*(1 + x) + sinh(x)). a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n > 5. a(n) = (1/2)*(-1 + n)^2*n - (-1 + n)*floor(n/2) + 2*floor(n/2)^2. a(n) = (1/2)*(-1 + n)^2*n - (-1 + n)*A004526(n) + 2*A000290(A004526(n)). a(n) = (n/2)*((n - 1)^2 + 1) for even n; a(n) = (n/2)*(n - 1)^2 otherwise. - Bruno Berselli, Feb 06 2019 a(n) = 2*A004526(n*A000982(n-1)). [Found by Christian Krause's LODA miner] - Stefano Spezia, Dec 12 2021 a(n) = 2*A005997(n-1) for n >= 2. - Hugo Pfoertner, Dec 13 2021 MAPLE a:=n->(1/2)*(-1 + n)^2*n - (-1 + n)*floor(n/2) + 2*(floor(n/2))^2: seq(a(n), n=0..50); MATHEMATICA a[n_] := 1/2 (-1 + n)^2 n - (-1 + n) Floor[n/2] + 2 Floor[n/2]^2; Array[a, 50, 0]; Table[n (2 (n - 2) n + (-1)^n + 3)/4, {n, 0, 50}] (* Bruno Berselli, Feb 06 2019 *) PROG (GAP) Flat(List([0..50], n->(1/2)*(-1 + n)^2*n - (-1 + n)*Int(n/2) + 2*(Int(n/2))^2)); (Magma) [(1/2)*(-1 + n)^2*n - (-1 + n)*Floor(n/2) + 2*(Floor(n/2))^2: n in [0..50]]; (Maxima) makelist((1/2)*(-1 + n)^2*n - (-1 + n)*floor(n/2) + 2*(floor(n/2))^2, n, 0, 50); (PARI) a(n) = (1/2)*(-1 + n)^2*n - (-1 + n)*floor(n/2) + 2*(floor(n/2))^2; (PARI) T(i, j, n) = if (i %2, j + n*(i-1), n*i - j + 1); a(n) = sum(k=1, n-1, T(k, k+1, n)); \\ Michel Marcus, Feb 06 2019 (Python) [int((1/2)*(-1 + n)**2*n - (-1 + n)*int(n/2) + 2*(int(n/2))**2) for n in range(0, 50)] CROSSREFS Cf. A000290, A000982, A004526, A005843, A005997, A317614, A322277, A323723, A325516. Sequence in context: A202963 A130315 A087150 * A214307 A087134 A036689 Adjacent sequences: A323721 A323722 A323723 * A323725 A323726 A323727 KEYWORD nonn,easy AUTHOR Stefano Spezia, Jan 25 2019 EXTENSIONS Definition by Bruno Berselli, Feb 06 2019 STATUS approved

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Last modified December 6 21:00 EST 2022. Contains 358648 sequences. (Running on oeis4.)