A152919 a(1)=1, for n>1, a(n) = n^2/4 + n/2 for even n, a(n) = n^2/4 + n - 5/4 for odd n.

1, 2, 4, 6, 10, 12, 18, 20, 28, 30, 40, 42, 54, 56, 70, 72, 88, 90, 108, 110, 130, 132, 154, 156, 180, 182, 208, 210, 238, 240, 270, 272, 304, 306, 340, 342, 378, 380, 418, 420, 460, 462, 504, 506, 550, 552, 598, 600, 648, 650, 700, 702, 754, 756, 810, 812, 868

Offset: 1

Author

Roger L. Bagula, Dec 15 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Programs

Mathematica

a[n_] := If[n == 1, 1, If[Mod[n, 2] == 0, n^2/4 + n/2, n^2/4 + n - 5/4]];
Table[a[n], {n, 1, 100}]

Formula

From Chai Wah Wu, Jun 09 2020: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 6.

G.f.: x*(x^5 - x^4 - x - 1)/((x - 1)^3*(x + 1)^2). (End)

From Bernard Schott, Jun 10 2020: (Start)

Bisections are:

a(1) = 1 and a(2k+1) = A028552(k) for k >= 1,

a(2k) = A002378(k) for k >= 1, hence,

a(2k+2) = a(2k+1) + 2 for k >= 1. (End)