A094200 a(n) = 16*n^4 + 32*n^3 + 36*n^2 + 20*n + 3.

3, 107, 699, 2547, 6803, 15003, 29067, 51299, 84387, 131403, 195803, 281427, 392499, 533627, 709803, 926403, 1189187, 1504299, 1878267, 2318003, 2830803, 3424347, 4106699, 4886307, 5772003, 6773003, 7898907, 9159699, 10565747

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(n,k) = (-1)*Sum_{i=1..k} Sum_{j=1..i} (-1)^floor(j*x(n)). Then a(n) = k is the least integer k > 0 such that f(n, k) = 0. In other words, f(n, a(n)) = 0, and if f(n,k) = 0, then a(n) <= k. [Edited by Petros Hadjicostas, Jul 12 2020]

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A085005, A094201.

Programs

Mathematica

Table[16n^4+32n^3+36n^2+20n+3,{n,0,30}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{3,107,699,2547,6803},30] (* Harvey P. Dale, Jul 23 2013 *)

PARI

a(n) = 16*n^4+32*n^3+36*n^2+20*n+3

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n >= 5. - Harvey P. Dale, Jul 23 2013