A194073 a(n) = 1 + floor((3/4)*n^2).

1, 4, 7, 13, 19, 28, 37, 49, 61, 76, 91, 109, 127, 148, 169, 193, 217, 244, 271, 301, 331, 364, 397, 433, 469, 508, 547, 589, 631, 676, 721, 769, 817, 868, 919, 973, 1027, 1084, 1141, 1201, 1261, 1324, 1387, 1453, 1519, 1588, 1657, 1729, 1801

Offset: 1

Author

Clark Kimberling, Aug 14 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A002620, A194074 (natural fractal sequence of A194073), A194075 (natural interspersion of A194074).

Programs

Mathematica

c[k_]:=1+Floor[(3/4)k^2];
Table[c[k],{k,1,90}]

PARI

a(n)=3*n^2\4+1 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = 1 + floor((3/4)*n^2).

G.f.: x*(1+2*x-x^2+x^3) / ( (1+x)*(1-x)^3 ). - R. J. Mathar, Aug 25 2011

a(n) = 1 + 3*A002620(n). - R. J. Mathar, Aug 25 2011

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - Wesley Ivan Hurt, Jun 26 2025