A098547 a(n) = n^3 + n^2 + 1.

1, 3, 13, 37, 81, 151, 253, 393, 577, 811, 1101, 1453, 1873, 2367, 2941, 3601, 4353, 5203, 6157, 7221, 8401, 9703, 11133, 12697, 14401, 16251, 18253, 20413, 22737, 25231, 27901, 30753, 33793, 37027, 40461, 44101, 47953, 52023, 56317, 60841, 65601

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Colin Barker, Aug 29 2014

G.f.: (1 - x + 7*x^2 - x^3)/(1-x)^4. - Colin Barker, Aug 29 2014

a(n) = A081423(n) + A000217(n-1). - Bruce J. Nicholson, Jan 06 2019

Maple

with(combinat): seq(fibonacci(3, n)+n^3, n=0..40); # Zerinvary Lajos, May 25 2008

Mathematica

Table[n^3+n^2+1, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)

Prog

(Magma) [(n^3+n^2+1): n in [1..60]]; // Vincenzo Librandi, Apr 06 2011
(PARI) Vec(-(x^3-7*x^2+x-1)/(x-1)^4 + O(x^100)) \\ Colin Barker, Aug 29 2014

Crossrefs

Cf. A000578, A066023, A001093, A034262, A071568, A011379, A027444, A053698, A033431, A033562, A061317.

Cf. A081423, A000217.

Sequence in context: A147168 A147183 A254955 * A256316 A194486 A024535

Adjacent sequences: A098544 A098545 A098546 * A098548 A098549 A098550

Keyword

nonn,easy

Author

Douglas Winston (douglas.winston(AT)srupc.com), Oct 26 2004

Status

approved