A106734 a(n) = n^3 - 7*n + 7.

1, 1, 13, 43, 97, 181, 301, 463, 673, 937, 1261, 1651, 2113, 2653, 3277, 3991, 4801, 5713, 6733, 7867, 9121, 10501, 12013, 13663, 15457, 17401, 19501, 21763, 24193, 26797, 29581, 32551, 35713, 39073, 42637, 46411, 50401, 54613, 59053, 63727

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

n*a(n) + n*(n-1)*7 = n^4.

G.f.: (1 - 3*x + 15*x^2 - 7*x^3)/(1-x)^4. - Harvey P. Dale, Feb 18 2018

E.g.f.: (7 - 6*x + 3*x^2 + x^3)*exp(x) - 7. - G. C. Greubel, Sep 11 2021

Example

a(2) = 1, 1 + 15 = 2^4;
a(3) = 13, 13 + 27 + 41 = 3^4;
a(4) = 43, 43 + 57 + 71 + 85 = 4^4.

Mathematica

Table[n^3-7n+7, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 1, 13, 43}, 40] (* Harvey P. Dale, Feb 18 2018 *)

Prog

(PARI) a(n) = n^3 - 7*n + 7; \\ Michel Marcus, Sep 05 2013
(Sage) [n*(n^2 -7) +7 for n in (0..40)] # G. C. Greubel, Sep 11 2021

Crossrefs

Cf. A105551.

Sequence in context: A031382 A187677 A082040 * A066465 A023262 A067260

Adjacent sequences: A106731 A106732 A106733 * A106735 A106736 A106737

Keyword

nonn,easy

Author

Andras Erszegi (erszegi.andras(AT)chello.hu), May 14 2005

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 16 2007

Status

approved