A038709 a(n) = floor(n*(n+1/2)/4).

0, 0, 1, 2, 4, 6, 9, 13, 17, 21, 26, 31, 37, 43, 50, 58, 66, 74, 83, 92, 102, 112, 123, 135, 147, 159, 172, 185, 199, 213, 228, 244, 260, 276, 293, 310, 328, 346, 365, 385, 405, 425, 446, 467, 489, 511, 534, 558, 582, 606, 631, 656, 682, 708, 735

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to Beatty sequences

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

Formula

a(n) = 2*a(n-1) - a(n-2) + a(n-8) - 2*a(n-9) + a(n-10) for n > 9. - Jinyuan Wang, Mar 16 2020

Mathematica

Table[Floor[n (n + 1 / 2) / 4], {n, 0, 60}] (* Vincenzo Librandi, Mar 17 2020 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 1, 2, 4, 6, 9, 13, 17, 21}, 80] (* Harvey P. Dale, Jan 11 2024 *)

Prog

(PARI) a(n) = floor(n*(n+1/2)/4); \\ Jinyuan Wang, Mar 16 2020
(Magma) [Floor(n * (n + 1 / 2) / 4): n in [0..60]]; // Vincenzo Librandi, Mar 17 2020

Crossrefs

Cf. A038707.

Sequence in context: A360393 A098387 A283525 * A186351 A049981 A194178

Adjacent sequences: A038706 A038707 A038708 * A038710 A038711 A038712

Keyword

nonn

Author

N. J. A. Sloane, May 02 2000

Status

approved