A059293 a(n) = round(n*(5*n - 14)/12) + 1.

1, 0, 0, 1, 3, 6, 9, 13, 18, 24, 31, 39, 47, 56, 66, 77, 89, 102, 115, 129, 144, 160, 177, 195, 213, 232, 252, 273, 295, 318, 341, 365, 390, 416, 443, 471, 499, 528, 558, 589, 621, 654, 687, 721, 756, 792, 829, 867, 905, 944, 984, 1025, 1067, 1110, 1153, 1197, 1242

Offset

0,5

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 122, see #19 (2), I(n).

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

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

Formula

From Chai Wah Wu, Jun 20 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8) for n > 7.

G.f.: (-3*x^7 + x^6 - x^5 - x^4 - x^3 - x^2 + 2*x - 1)/( (x+1)*(x^2+x+1)*(x^2-x+1)*(x-1)^3). (End)

Mathematica

Table[Round[n*(5*n - 14)/12], {n, 0, 10}] + 1 (* G. C. Greubel, Jan 04 2017 *)
LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 1}, {1, 0, 0, 1, 3, 6, 9, 13}, 60] (* Harvey P. Dale, Mar 06 2022 *)

Prog

(PARI) a(n) = { round(n*(5*n - 14)/12) + 1 } \\ Harry J. Smith, Jun 25 2009
(Magma) [Round(n*(5*n-14)/12)+1: n in [0..60]]; // Vincenzo Librandi, Jan 05 2017

Crossrefs

Sequence in context: A132352 A033436 A002578 * A129728 A307270 A310160

Adjacent sequences: A059290 A059291 A059292 * A059294 A059295 A059296

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Jan 25 2001

Status

approved