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 A323723 a(n) = (-2 - (-1)^n*(-2 + n) + n + 2*n^3)/4. 4
 0, 0, 4, 14, 32, 64, 108, 174, 256, 368, 500, 670, 864, 1104, 1372, 1694, 2048, 2464, 2916, 3438, 4000, 4640, 5324, 6094, 6912, 7824, 8788, 9854, 10976, 12208, 13500, 14910, 16384, 17984, 19652, 21454, 23328, 25344, 27436, 29678, 32000, 34480, 37044, 39774 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For n > 1, a(n) is the subdiagonal sum of the matrix M(n) whose permanent is A322277(n). All the terms of this sequence are even numbers (A005843). 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*(2 + 3*x + x^3)/((1 - x)^4*(1 + x)^2). E.g.f.: (1/4)*exp(-x)*(2 + x)*(1 + exp(2*x)*(-1 + 2*x + 2* x^2)). 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) = (6 + n + n^3 + 12*floor((n - 3)/2) + 4*floor((n - 3)/2)^2 - 2*(1 + n)*floor((n - 1)/2)/2 a(n) = (-2 - A033999(n)*(-2 + n) + n + A033431(n))/4. a(n) = n^3/2 for even n; a(n) = (n - 1)*(n^2 + n + 2)/2 otherwise. - Bruno Berselli, Feb 06 2019 MAPLE a:=n->(-2 - (-1)^n*(-2 + n) + n + 2*n^3)/4: seq(a(n), n=0..50); MATHEMATICA a[n_]:=(6 + n + n^3 + 12 Floor[1/2 (-3 + n)] + 4 Floor[1/2 (-3 + n)]^2 - 2 (1 + n) Floor[1/2 (-1 + n)])/2; Array[a, 50, 0] PROG (GAP) Flat(List([0..50], n -> (-2-(-1)^n*(-2+n)+n+2*n^3)/4)); (MAGMA) [(-2-(-1)^n*(-2+n)+n+2*n^3)/4: n in [0..50]]; (Maxima) makelist((-2-(-1)^n*(-2+n)+n+2*n^3)/4, n, 0, 50); (PARI) a(n) = (-2-(-1)^n*(-2+n)+n+2*n^3)/4; (Python) [(-2-(-1)**n*(-2+n)+n+2*n**3)/4 for n in range(50)] CROSSREFS Cf. A005843, A033431, A033999, A317614, A322277, A323724, A325655. Sequence in context: A036486 A023627 A023649 * A324042 A099590 A078432 Adjacent sequences:  A323720 A323721 A323722 * A323724 A323725 A323726 KEYWORD nonn,easy AUTHOR Stefano Spezia, Jan 25 2019 STATUS approved

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Last modified January 29 11:16 EST 2020. Contains 331337 sequences. (Running on oeis4.)