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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
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 (list; graph; refs; listen; history; text; internal format)
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). [From R. J. Mathar, May 24 2010]

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]

PROG

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

CROSSREFS

Sequence in context: A115266 A164508 A292774 * A004978 A005282 A046185

Adjacent sequences:  A026036 A026037 A026038 * A026040 A026041 A026042

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified June 19 17:22 EDT 2018. Contains 305594 sequences. (Running on oeis4.)