A026056 a(n) = (d(n)-r(n))/5, where d = A026054 and r is the periodic sequence with fundamental period (3,3,0,0,4).

2, 5, 10, 16, 23, 33, 45, 60, 77, 96, 119, 145, 175, 208, 244, 285, 330, 380, 434, 492, 556, 625, 700, 780, 865, 957, 1055, 1160, 1271, 1388, 1513, 1645, 1785, 1932, 2086, 2249, 2420, 2600, 2788, 2984, 3190, 3405, 3630, 3864, 4107, 4361, 4625, 4900, 5185, 5480, 5787, 6105, 6435, 6776, 7128, 7493

Offset

3,1

Links

Table of n, a(n) for n=3..58.

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

Formula

a(n) = (n + 2)*(n + 3)*(n + 13)/30 - 1/5*(2 + (1/2 + 7/10*5^(1/2))*cos(2*n*Pi/5) + ( - 1/10*2^(1/2)*(5 + 5^(1/2))^(1/2))*sin(2*n*Pi/5) + (1/2 - 7/10*5^(1/2))*cos(4*n*Pi/5) + ( - 1/10*2^(1/2)*(5 - 5^(1/2))^(1/2))*sin(4*n*Pi/5)). - Richard Choulet, Dec 14 2008

G.f.: x^3*( 2-x+x^2-x^3 ) / ( (x^4+x^3+x^2+x+1)*(x-1)^4 ). - R. J. Mathar, Jun 22 2013

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). - Wesley Ivan Hurt, Jul 29 2022

Crossrefs

Cf. A152893, A026054.

Sequence in context: A086849 A131938 A031871 * A267159 A084587 A001859

Adjacent sequences: A026053 A026054 A026055 * A026057 A026058 A026059

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved