A026045 a(n) = (d(n)-r(n))/5, where d = A026043 and r is the periodic sequence with fundamental period (0,2,3,0,0).

9, 13, 19, 28, 39, 53, 70, 91, 117, 147, 182, 222, 268, 321, 380, 446, 519, 600, 690, 788, 895, 1011, 1137, 1274, 1421, 1579, 1748, 1929, 2123, 2329, 2548, 2780, 3026, 3287, 3562, 3852, 4157, 4478, 4816, 5170, 5541, 5929, 6335, 6760, 7203, 7665, 8146, 8647, 9169, 9711, 10274, 10858, 11464

Offset

1,1

Links

Table of n, a(n) for n=1..53.

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

Formula

a(n)=(n + 5)*(2*n^2 + 11*n + 54)/30 - (1 + ( - 1/2 - 1/10*5^(1/2))*cos(2*n*Pi/5) + (1/10*(3*(5 - 5^(1/2))^(1/2) + 2*(5 + 5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5) + (1/10*5^(1/2) - 1/2)*cos(4*n*Pi/5) + (1/10*(2*(5 - 5^(1/2))^(1/2) - 3*(5 + 5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5))/5 - Richard Choulet, Dec 14 2008

G.f. x*( 9-14*x+7*x^2+x^3-x^4-8*x^5-6*x^7+14*x^6 ) / ( (x^4+x^3+x^2+x+1)*(x-1)^4 ). - R. J. Mathar, Jun 22 2013

a(n) ~ n^3/15. - Charles R Greathouse IV, Jun 02 2026

Mathematica

LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {9, 13, 19, 28, 39, 53, 70, 91}, 60] (* Harvey P. Dale, May 14 2026 *)

Prog

(PARI) a(n)=(2*n^3+15*n^2+73*n+28537855\31^(n%5)%31*6)/30 \\ Charles R Greathouse IV, Jun 02 2026

Crossrefs

A152857 - Richard Choulet, Dec 14 2008

Cf. A026043.

Sequence in context: A307287 A373781 A373914 * A371728 A304259 A124249

Adjacent sequences: A026042 A026043 A026044 * A026046 A026047 A026048

Keyword

nonn,easy,changed

Author

Clark Kimberling

Status

approved