A008738 a(n) = floor((n^2 + 1)/5).

0, 0, 1, 2, 3, 5, 7, 10, 13, 16, 20, 24, 29, 34, 39, 45, 51, 58, 65, 72, 80, 88, 97, 106, 115, 125, 135, 146, 157, 168, 180, 192, 205, 218, 231, 245, 259, 274, 289, 304, 320, 336, 353, 370, 387, 405, 423, 442, 461, 480, 500, 520, 541, 562, 583, 605, 627, 650, 673

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Without initial zeros, Molien series for 3-dimensional group [2+,n] = 2*(n/2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Index entries for Molien series
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Crossrefs

Cf. A011858. Partial sums of A288156.

Programs

GAP

List([0..60], n-> Int((n^2 + 1)/5)); # G. C. Greubel, Aug 03 2019

Magma

[(n^2+1) div 5: n in [0..60]]; // Bruno Berselli, Oct 28 2011

Mathematica

Floor[(Range[0,60]^2 + 1)/5] (* G. C. Greubel, Aug 03 2019 *)

PARI

a(n)=(n^2+1)\5;

Sage

[floor((n^2+1)/5) for n in (0..60)] # G. C. Greubel, Aug 03 2019

Formula

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

a(n+2)= A249020(n) + A249020(n-1). - R. J. Mathar, Aug 11 2021

Extensions

More terms from Philip Mummert (s1280900(AT)cedarville.edu), May 10 2000