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 A281151 a(n) = floor(4*n*(n+1)/5). 2
 0, 1, 4, 9, 16, 24, 33, 44, 57, 72, 88, 105, 124, 145, 168, 192, 217, 244, 273, 304, 336, 369, 404, 441, 480, 520, 561, 604, 649, 696, 744, 793, 844, 897, 952, 1008, 1065, 1124, 1185, 1248, 1312, 1377, 1444, 1513, 1584, 1656, 1729, 1804, 1881, 1960, 2040, 2121, 2204, 2289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1). FORMULA O.g.f.: x*(1 + x^2)*(1 + x)^2/((1 - x)^3*(1 + x + x^2 + x^3 + x^4)). a(n) = a(-n-1) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) = a(n-5) + 8*(n-2). a(5*k+r) = 20*k^2 + 4*(2*r+1)*k + r^2, where 0 <= r <= 4. Example: for r=3, a(5*k+3) = (2*k+1)*(10*k+9), which gives: 9, 57, 145, 273, 441, 649 etc. Also, a(n) belongs to A047462, in fact: for r = 0 or 4, a(n) == 0 (mod 8); for r = 1 or 3, a(n) == 1 (mod 8); for r = 2, a(n) == 4 (mod 8). a(n) = a(-n) + A047462(n). a(n) = n^2 - floor((n-2)^2/5). MATHEMATICA Table[Floor[4 n (n + 1)/5], {n, 0, 60}] PROG (PARI) vector(60, n, n--; floor(4*n*(n+1)/5)) (Python) [int(4*n*(n+1)/5) for n in range(60)] (Sage) [floor(4*n*(n+1)/5) for n in range(60)] (Maxima) makelist(floor(4*n*(n+1)/5), n, 0, 60); (MAGMA) [4*n*(n+1) div 5: n in [0..60]]; CROSSREFS Subsequence of A047462. Partial sums of A047486. Cf. A184005: n^2 - floor((n-2)^2/4). Cf. sequences with formula floor(k*n*(n+1)/(k+1)): A000217 (k=1), A143978 (k=2), A281026 (k=3), this sequence (k=4), A194275 (k=5). Sequence in context: A161697 A078593 A168350 * A337722 A052117 A033611 Adjacent sequences:  A281148 A281149 A281150 * A281152 A281153 A281154 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 16 2017 STATUS approved

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Last modified May 6 17:45 EDT 2021. Contains 343586 sequences. (Running on oeis4.)