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A367965
a(n) = (1/8)*(4*n^2 + 6*n + (-1)^n*(2*n*(n + 1) - 1) + 1).
1
0, 1, 5, 4, 16, 9, 33, 16, 56, 25, 85, 36, 120, 49, 161, 64, 208, 81, 261, 100, 320, 121, 385, 144, 456, 169, 533, 196, 616, 225, 705, 256, 800, 289, 901, 324, 1008, 361, 1121, 400, 1240, 441, 1365, 484, 1496, 529, 1633, 576, 1776, 625, 1925, 676, 2080, 729, 2241, 784
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n - k) * A367964(n, k).
a(2*n) = n*(3*n+2) = A045944(n).
a(2*n-1) = n^2 = A000290(n).
G.f.: x*(1 + 5*x + x^2 + x^3)/(1 - x)^3*(1 + x)^3). - Stefano Spezia, Dec 07 2023
MAPLE
a := n -> (1/8)*(4*n^2 + 6*n + (-1)^n*(2*n*(n + 1) - 1) + 1):
seq(a(n), n = 0..55);
MATHEMATICA
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 5, 4, 16, 9}, 100] (* Paolo Xausa, Dec 07 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Dec 07 2023
STATUS
approved