A213299 Partial sums of A211681.

2, 5, 10, 17, 40, 77, 130, 203, 440, 813, 1350, 2087, 4460, 8197, 13570, 20943, 44680, 82053, 135790, 209527, 446900, 820637, 1358010, 2095383, 4469120, 8206493, 13580230, 20953967, 44691340

Offset: 1

Author

Hieronymus Fischer, Jun 08 2012

Keywords

• nonn
• easy
• base

Comments

The terms are primes for n = 1, 2, 4, 12, 22, 32 and possibly further n’s (Question).

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..100
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,9,-18,9,0,10,-20,10).

Crossrefs

Cf. A019546, A035232, A039996, A046034, A085823, A211681, A211682.

Formula

a(n) = ((3982 + 2709*k + 567*k^2 + 54*k^3)*10^m - 1980*m - 2200 - 495*k + 162*((n+1) mod 2) * (-1)^m * (-1)^floor(n/2))/891, where m=floor((n-1)/4), k=(n-1) mod 4.

G.f.: (2*x*(1+x^10) + 3*x^2*(1 + x^3 + x^5 + x^6) + 5*x^3*(1+x^6) + 7*x^4*(1+x^2))/((1-x)*(1-10*x^4)*(1-x^8)).

From Chai Wah Wu, Feb 08 2023: (Start)

a(n) = 2*a(n-1) - a(n-2) + 9*a(n-4) - 18*a(n-5) + 9*a(n-6) + 10*a(n-8) - 20*a(n-9) + 10*a(n-10) for n > 10.

G.f.: x*(-2*x^7 + 2*x^6 - 5*x^5 + 2*x^4 - 2*x^3 - 2*x^2 - x - 2)/((x - 1)^2*(x^4 + 1)*(10*x^4 - 1)). (End)

Extensions

Typo in g.f. corrected by Hieronymus Fischer, Sep 03 2012