A055804 a(n) = T(n,n-4), array T as in A055801.

1, 1, 1, 2, 3, 5, 8, 12, 19, 26, 40, 51, 76, 92, 133, 155, 218, 247, 339, 376, 505, 551, 726, 782, 1013, 1080, 1378, 1457, 1834, 1926, 2395, 2501, 3076, 3197, 3893, 4030, 4863, 5017, 6004, 6176, 7335, 7526, 8876, 9087

Offset: 4

Author

Clark Kimberling, May 28 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A055801, A055802, A055803, A055805, A055806.

Programs

GAP

Concatenation([1], List([5..50], n-> (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 )); # G. C. Greubel, Jan 24 2020

Magma

[1] cat [(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768: n in [5..50]]; // G. C. Greubel, Jan 24 2020

Maple

seq( `if`(n=4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768), n=4..50); # G. C. Greubel, Jan 24 2020

Mathematica

Table[If[n==4, 1, (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768], {n,4,50}] (* G. C. Greubel, Jan 24 2020 *)

PARI

vector(50, n, my(m=n+3); if(m==4, 1, (2*m^4 -28*m^3 +178*m^2 -416*m +441 +(-1)^m*(4*m^3 -90*m^2 + 704*m -1977))/768)) \\ G. C. Greubel, Jan 24 2020

Sage

[1]+[(2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n in (5..50)] # G. C. Greubel, Jan 24 2020

Formula

G.f.: x^4*(-1 +4*x^2 -x^3 -7*x^4 +2*x^5 +5*x^6 -2*x^7 -2*x^8 +x^9)/((1-x)^5 (1+x)^4). - R. J. Mathar, Jul 10 2012

From G. C. Greubel, Jan 24 2020: (Start)

a(n) = (2*n^4 -28*n^3 +178*n^2 -416*n +441 +(-1)^n*(4*n^3 -90*n^2 + 704*n -1977))/768 for n>4, with a(4) = 1.

E.g.f.: ( (768 -768*x +192*x^2 -64*x^3 +16*x^4) +(-768 -441*x +15*x^2 -10*x^3 +x^4)*cosh(x) +(1209 +177*x +93*x^2 -6*x^3 +x^4)*sinh(x) )/384. (End)