A027968 a(n) = T(n, 2*n-6), T given by A027960.

1, 4, 11, 29, 73, 171, 370, 743, 1397, 2482, 4201, 6821, 10685, 16225, 23976, 34591, 48857, 67712, 92263, 123805, 163841, 214103, 276574, 353511, 447469, 561326, 698309, 862021, 1056469, 1286093, 1555796, 1870975, 2237553

Offset: 3

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

A column of triangle A026998.

Programs

GAP

List([3..40], n-> (-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720) # G. C. Greubel, Jul 01 2019

Magma

[(-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720: n in [3..40]]; // G. C. Greubel, Jul 01 2019

Mathematica

Table[(-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720, {n,3,40}] (* G. C. Greubel, Jul 01 2019 *)

PARI

for(n=3,40, print1((-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720, ", ")) \\ G. C. Greubel, Jul 01 2019

Sage

[(-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720 for n in (3..40)] # G. C. Greubel, Jul 01 2019

Formula

From Ralf Stephan, Feb 07 2004: (Start)

G.f.: x^3*(1 -3*x +4*x^2 +x^3 -4*x^4 +3*x^5 -x^6)/(1-x)^7.

a(n) = A027969(n+1) - A027969(n). (End)

From G. C. Greubel, Jul 01 2019: (Start)

a(n) = (-7920 +7548*n -3176*n^2 +735*n^3 -65*n^4 -3*n^5 +n^6)/720.

E.g.f.: (7920 +2880*x +360*x^2 -(7920 -5040*x +1440*x^2 -360*x^3 +30*x^4 -12*x^5 -x^6)*exp(x))/6!. (End)