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

1,2

Links

Table of n, a(n) for n=1..57.

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

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)

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}]

Crossrefs

Sequence in context: A167856 A293750 A162578 * A306564 A002088 A092249

Adjacent sequences: A152916 A152917 A152918 * A152920 A152921 A152922

Keyword

nonn,easy

Author

Roger L. Bagula, Dec 15 2008

Status

approved