A094201 a(n) = 4*n^5 + 10*n^4 + 13*n^3 + 11*n^2 + 5*n + 1.

1, 44, 447, 2248, 7685, 20676, 47299, 96272, 179433, 312220, 514151, 809304, 1226797, 1801268, 2573355, 3590176, 4905809, 6581772, 8687503, 11300840, 14508501, 18406564, 23100947, 28707888, 35354425, 43178876, 52331319

Offset: 0

Author

Benoit Cloitre, May 25 2004

Keywords

• nonn
• easy

Comments

Let x(n) = (1/2)*(-(2*n+1) + sqrt((2*n+1)^2 + 4)) and f(k) = (-1)*(Sum_{i=1..k} Sum_{j=1..i} (-1)^floor(j*x(n))), then a(n) = Max{f(k): 0 < k < A094200(n)}.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A085005, A094200.

Programs

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{1,44,447,2248,7685,20676},30] (* Harvey P. Dale, Oct 23 2021 *)

PARI

a(n)=4*n^5+10*n^4+13*n^3+11*n^2+5*n+1

Formula

G.f.: (37*x^4 + 206*x^3 + 198*x^2 + 38*x + 1)/(x - 1)^6. - Jinyuan Wang, Apr 06 2020

Extensions

Corrected by T. D. Noe, Nov 09 2006