A011869 a(n) = floor(n*(n-1)/16).

0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 17, 19, 21, 23, 26, 28, 31, 34, 37, 40, 43, 47, 50, 54, 58, 62, 66, 70, 74, 78, 83, 87, 92, 97, 102, 107, 112, 118, 123, 129, 135, 141, 147, 153, 159, 165, 172, 178, 185, 192, 199, 206, 213, 221, 228, 236, 244, 252, 260

Offset

0,8

Links

Matthew House, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-3,1).

Formula

G.f.: -((x^5 (1-x+x^2) (1-x+x^2-x^3+x^4-x^5+x^6))/((-1+x)^3 (1+x^2) (1+x^4) (1+x^8)))

a(n) = n^2/16 - n/16 + O(1). - Charles R Greathouse IV, May 31 2026

Mathematica

Table[Floor[(n(n-1))/16], {n, 0, 70}] (* or *) LinearRecurrence[{3, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1}, {0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15}, 70] (* Harvey P. Dale, May 23 2019 *)

Prog

(Magma) [(n*(n-1) div 16) : n in [0..70]]; // Vincenzo Librandi, May 26 2019
(PARI) a(n)=n*(n-1)\16 \\ Charles R Greathouse IV, May 31 2026

Crossrefs

Cf. A011861.

Sequence in context: A191886 A184115 A050418 * A177738 A134030 A226189

Adjacent sequences: A011866 A011867 A011868 * A011870 A011871 A011872

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved