A026039 a(n) = (d(n) - r(n))/5, where d = A026037 and r is the periodic sequence with fundamental period (1,2,0,2,0).

2, 4, 8, 13, 21, 31, 44, 61, 81, 106, 135, 169, 209, 254, 306, 364, 429, 502, 582, 671, 768, 874, 990, 1115, 1251, 1397, 1554, 1723, 1903, 2096, 2301, 2519, 2751, 2996, 3256, 3530, 3819, 4124, 4444, 4781, 5134, 5504, 5892, 6297, 6721, 7163, 7624, 8105, 8605, 9126, 9667, 10229, 10813, 11418, 12046, 12696, 13369

Offset

3,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).

Formula

a(n) = (n + 3)*(2*n^2 + 9*n + 22)/30 - 1/5 - (-1/25*((5 - 5^(1/2))^(1/2) - (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5) - (1/25*((5 - 5^(1/2))^(1/2) + (5 + 5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5). - Richard Choulet, Dec 14 2008

a(n) = round((2*n-1)*(n^2-n+6)/30) = floor((2*n^3-3*n^2+13*n)/30) = ceiling((n-1)*(2*n^2-n+12)/30) = round((n-1)*(2*n^2-n+12)/30). - Mircea Merca, Dec 03 2010

From R. J. Mathar, May 24 2010: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).

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

a(n) = a(n-5) + n^2 - 6*n + 13, n > 5, a(1)=0, a(2)=1. - Mircea Merca, Dec 03 2010

Mathematica

f[n_] := Round[(2 n - 1)*(n^2 - n + 6)/30]; Array[f, 57, 3]
LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {2, 4, 8, 13, 21, 31, 44, 61}, 60] (* Harvey P. Dale, Sep 05 2023 *)

Prog

(Magma) [Round((2*n-1)*(n^2-n+6)/30): n in [3..60]]; // Vincenzo Librandi, Jun 25 2011

Crossrefs

Cf. A026037.

Sequence in context: A164508 A308094 A292774 * A004978 A005282 A046185

Adjacent sequences: A026036 A026037 A026038 * A026040 A026041 A026042

Keyword

nonn

Author

Clark Kimberling

Status

approved