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URL: https://oeis.org/A381816

⇱ A381816 - OEIS

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A381816
a(n) = (4*n^2 - (-1)^n - 2*n - 7)/4.
1
-1, 1, 6, 12, 21, 31, 44, 58, 75, 93, 114, 136, 161, 187, 216, 246, 279, 313, 350, 388, 429, 471, 516, 562, 611, 661, 714, 768, 825, 883, 944, 1006, 1071, 1137, 1206, 1276, 1349, 1423, 1500, 1578, 1659, 1741, 1826, 1912, 2001, 2091, 2184, 2278, 2375, 2473
OFFSET
1,3
COMMENTS
a(n) is also the graph bandwidth of the n X n rook complement graph for n == 2 and n > 3.
LINKS
Eric Weisstein's World of Mathematics, Graph Bandwidth.
Eric Weisstein's World of Mathematics, Rook Complement Graph.
FORMULA
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).
G.f.: x^2*(-1-4*x+x^3)/((-1+x)^3*(1+x)).
MATHEMATICA
Table[(4 n^2 - (-1)^n - 2 n - 7)/4, {n, 2, 20}]
LinearRecurrence[{2, 0, -2, 1}, {-1, 1, 6, 12}, 20]
CoefficientList[Series[(-1 - 4 x + x^3)/((-1 + x)^3 (1 + x)), {x, 0, 20}], x]
PROG
(Python)
def A381816(n): return (n+1)*((n<<1)-3)-(n&1^1)>>1 # Chai Wah Wu, Mar 07 2025
CROSSREFS
Sequence in context: A371145 A370989 A055458 * A360570 A178733 A344033
KEYWORD
sign,easy
AUTHOR
Eric W. Weisstein, Mar 07 2025
STATUS
approved