A026042 a(n) = (d(n)-r(n))/5, where d = A026040 and r is the periodic sequence with fundamental period (4,0,4,3,4).

4, 8, 12, 19, 28, 40, 56, 74, 97, 124, 156, 194, 236, 285, 340, 402, 472, 548, 633, 726, 828, 940, 1060, 1191, 1332, 1484, 1648, 1822, 2009, 2208, 2420, 2646, 2884, 3137, 3404, 3686, 3984, 4296, 4625, 4970, 5332, 5712, 6108, 6523, 6956, 7408, 7880, 8370, 8881, 9412, 9964, 10538, 11132, 11749

Offset

1,1

Links

Table of n, a(n) for n=1..54.

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

Formula

a(n)=(n + 4)*(n^2 + 5*n + 18)/15 - 3/5 - (1/2 - 3/10*5^(1/2))/5*cos(2*n*Pi/5) + (1/10*(4*(5 + 5^(1/2))^(1/2) - (5 - 5^(1/2))^(1/2))*2^(1/2))/5*sin(2*n*Pi/5) - (3/10*5^(1/2) + 1/2)/5*cos(4*n*Pi/5) + (1/10*((5 + 5^(1/2))^(1/2) + 4*(5 - 5^(1/2))^(1/2))*2^(1/2))/5*sin(4*n*Pi/5) - Richard Choulet, Dec 14 2008

G.f. x*( 4-4*x+3*x^3-x^4-3*x^5+5*x^6-2*x^7 ) / ( (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 01 2026

Prog

(PARI) a(n)=(n^3+6*n^2+23*n+87711\13^(n%5)%13)/15 + 2 \\ Charles R Greathouse IV, Jun 01 2026

Crossrefs

Cf. A152856, A026040.

Sequence in context: A287402 A311648 A337746 * A196377 A180603 A311649

Adjacent sequences: A026039 A026040 A026041 * A026043 A026044 A026045

Keyword

nonn,easy,changed

Author

Clark Kimberling

Status

approved