A055810 a(n) = T(n,n-5), array T as in A055807.

1, 31, 80, 160, 280, 450, 681, 985, 1375, 1865, 2470, 3206, 4090, 5140, 6375, 7815, 9481, 11395, 13580, 16060, 18860, 22006, 25525, 29445, 33795, 38605, 43906, 49730, 56110, 63080, 70675, 78931, 87885, 97575

Offset: 5

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 5..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A055807, A055809, A055811, A055815, A055816, A055817.

Programs

GAP

Concatenation([1], List([6..40], n-> (240 -54*n -49*n^2 +6*n^3 +n^4)/24 )); # G. C. Greubel, Jan 23 2020

Magma

[1] cat [(240 -54*n -49*n^2 +6*n^3 +n^4)/24: n in [6..40]]; // G. C. Greubel, Jan 23 2020

Maple

seq( `if`(n=5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24), n=5..40); # G. C. Greubel, Jan 23 2020

Mathematica

Table[If[n==5, 1, (240 -54*n -49*n^2 +6*n^3 +n^4)/24], {n,5,40}] (* G. C. Greubel, Jan 23 2020 *)

PARI

vector(40, n, my(m=n+4); if(m==5, 1, (240 -54*m -49*m^2 +6*m^3 +m^4)/24)) \\ G. C. Greubel, Jan 23 2020

Sage

[1]+[(240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n in (6..40)] # G. C. Greubel, Jan 23 2020

Formula

G.f.: x^5*(1 +26*x -65*x^2 +60*x^3 -25*x^4 +4*x^5)/(1-x)^5. - Colin Barker, Feb 22 2012

From G. C. Greubel, Jan 23 2020: (Start)

a(n) = (240 -54*n -49*n^2 +6*n^3 +n^4)/24 for n > 5, with a(5) = 1.

E.g.f.: (-1200 -720*x +100*x^3 +25*x^4 -4*x^5 + (1200 -480*x -120*x^2 +60*x^3 +5*x^4)*exp(x))/120. (End)