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A354594
a(n) = n^2 + 2*floor(n/2)^2.
4
0, 1, 6, 11, 24, 33, 54, 67, 96, 113, 150, 171, 216, 241, 294, 323, 384, 417, 486, 523, 600, 641, 726, 771, 864, 913, 1014, 1067, 1176, 1233, 1350, 1411, 1536, 1601, 1734, 1803, 1944, 2017, 2166, 2243, 2400, 2481, 2646, 2731, 2904
OFFSET
0,3
COMMENTS
The first bisection is A033581, the second bisection is A080859. - Bernard Schott, Jun 07 2022
FORMULA
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), n >= 5.
a(n) = A000290(n) + 2*A008794(n).
G.f.: x*(1 + 5*x + 3*x^2 + 3*x^3)/((1 - x)^3*(1 + x)^2).
E.g.f.: (x*(1 + 3*x)*cosh(x) + (1 + 3*x + 3*x^2)*sinh(x))/2. - Stefano Spezia, Jun 07 2022
MATHEMATICA
a[n_] := n^2 + 2 Floor[n/2]^2
Table[a[n], {n, 0, 90}] (* A354594 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 6, 11, 24}, 60]
PROG
(PARI) a(n) = n^2 + 2*(n\2)^2;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Lovler, Jun 01 2022
STATUS
approved