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

0,1

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

Table of n, a(n) for n=0..28.

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

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

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 *)

Prog

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

Crossrefs

Cf. A085005, A094201.

Sequence in context: A301369 A142509 A023325 * A003705 A146214 A261997

Adjacent sequences: A094197 A094198 A094199 * A094201 A094202 A094203

Keyword

nonn,easy

Author

Benoit Cloitre, May 25 2004

Status

approved