A173562 a(n) = n^2 + floor(n/4).

0, 1, 4, 9, 17, 26, 37, 50, 66, 83, 102, 123, 147, 172, 199, 228, 260, 293, 328, 365, 405, 446, 489, 534, 582, 631, 682, 735, 791, 848, 907, 968, 1032, 1097, 1164, 1233, 1305, 1378, 1453, 1530, 1610, 1691, 1774, 1859, 1947, 2036, 2127, 2220, 2316, 2413, 2512

Offset: 0

Author

Reinhard Zumkeller, Feb 21 2010

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Crossrefs

Cf. A000290, A002265, A002378, A035608, A047624, A057353.

Programs

Magma

[Floor((n + 1/8)^2) : n in [0..80]]; // Wesley Ivan Hurt, Jun 04 2016

Maple

A173562:=n->floor((n + 1/8)^2): seq(A173562(n), n=0..80); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Table[n^2+Floor[n/4],{n,0,50}] (* or *) LinearRecurrence[{2,-1,0,1,-2,1}, {0,1,4,9,17,26}, 50] (* Harvey P. Dale, Nov 25 2011 *)

PARI

a(n)=n^2+n\4 \\ Charles R Greathouse IV, Oct 16 2015

Python

def A173562(n): return n**2+(n>>2) # Chai Wah Wu, Feb 02 2023

Formula

a(n) = A002378(n)-A057353(n) = A035608(n)-A002265(n+2) = A000290(n)+A002265(n);

a(n+1) - a(n) = A047624(n+2).

a(n) = floor((n + 1/8)^2).

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

G.f.: x*(1+2*x+2*x^2+3*x^3)/((1+x)*(x^2+1)*(1-x)^3). - R. J. Mathar, Feb 27 2010

a(n) = (8*n^2+2*n-3+i^(2*n)+(1+i)*i^(-n)+(1-i)*i^n)/8 where i=sqrt(-1). - Wesley Ivan Hurt, Jun 04 2016