A301647 a(n) = n^3 - (n mod 2).
0, 8, 26, 64, 124, 216, 342, 512, 728, 1000, 1330, 1728, 2196, 2744, 3374, 4096, 4912, 5832, 6858, 8000, 9260, 10648, 12166, 13824, 15624, 17576, 19682, 21952, 24388, 27000, 29790, 32768, 35936, 39304, 42874, 46656, 50652, 54872, 59318, 64000, 68920, 74088, 79506, 85184, 91124
Offset: 1
Links
- Eric Weisstein's World of Mathematics, Graph Circumference
- Eric Weisstein's World of Mathematics, Grid Graph
- Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).
Crossrefs
Cf. A137932 (circumference of n X n grid graph).
Programs
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GAP
List([1..50],n->n^3- n mod 2); # Muniru A Asiru, Mar 25 2018
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Maple
seq(n^3-modp(n,2), n=1..50); # Muniru A Asiru, Mar 25 2018
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Mathematica
Table[n^3 - Mod[n, 2], {n, 20}] Table[(2 n^3 + (-1)^n - 1)/2, {n, 20}] LinearRecurrence[{3, -2, -2, 3, -1}, {0, 8, 26, 64, 124}, 20] CoefficientList[Series[2 x (4 + x + x^2)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x] -
PARI
a(n) = n^3 - (n%2); \\ Altug Alkan, Mar 25 2018
Formula
a(n) = (2 n^3 + (-1)^n - 1)/2.
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
G.f.: 2*x^2*(4 + x + x^2)/((-1 + x)^4*(1 + x)).
Comments