A094201 - OEIS

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

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OFFSET

0,2

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

Table of n, a(n) for n=0..26.

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

FORMULA

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A085005, A094200.

Sequence in context: A250336 A250337 A002613 * A210426 A231242 A221730