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

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A152893, A026054.

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