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

Author

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

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A105551.

Programs

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 *)

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

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

Extensions

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