A055802 a(n) = T(n,n-2), array T as in A055801.

1, 1, 1, 2, 3, 4, 6, 7, 10, 11, 15, 16, 21, 22, 28, 29, 36, 37, 45, 46, 55, 56, 66, 67, 78, 79, 91, 92, 105, 106, 120, 121, 136, 137, 153, 154, 171, 172, 190, 191, 210, 211, 231, 232, 253, 254, 276, 277, 300, 301, 325, 326, 351, 352, 378, 379, 406, 407, 435

Offset: 2

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Comments

For n>2, a(n)+a(n+1) seems to be A002620(n+1)+1.

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A002620, A134519.

Cf. A055801, A055803, A055804, A055805, A055806.

Programs

GAP

Concatenation([1], List([3..65], n-> (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16 )); # G. C. Greubel, Jan 23 2020

Magma

[1] cat [(2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16: n in [3..65]]; // G. C. Greubel, Jan 23 2020

Maple

seq( `if`(n==2, 1, (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16), n=2..65); # G. C. Greubel, Jan 23 2020

Mathematica

CoefficientList[Series[(1 -2*x^2 +x^3 +2*x^4 -x^5)/((1-x)^3*(1+x)^2), {x,0,65}], x] (* Wesley Ivan Hurt, Jan 20 2017 *)
Table[If[n==2,1, (2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16], {n,2,65}] (* G. C. Greubel, Jan 23 2020 *)

PARI

Vec(x^2*(1-2*x^2+x^3+2*x^4-x^5)/((1-x)^3*(1+x)^2) + O(x^65)) \\ Charles R Greathouse IV, Feb 03 2013

PARI

vector(65, n, my(m=n+1); if(m==2, 1, (2*m^2 -6*m +11 +(-1)^m*(2*m -11))/16)) \\ G. C. Greubel, Jan 23 2020

Sage

[1]+[(2*n^2 -6*n +11 +(-1)^n*(2*n -11))/16 for n in (3..65)] # G. C. Greubel, Jan 23 2020

Formula

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

a(n) = A114220(n-1), n>=3. - R. J. Mathar, Feb 03 2013

From Colin Barker, Jan 27 2016: (Start)

a(n) = (2*n^2 +2*(-1)^n*n -6*n -11*(-1)^n +11)/16 for n>2.

a(n) = (n^2 - 2*n)/8 for n>2 and even.

a(n) = (n^2 - 4*n + 11)/8 for n odd. (End)

E.g.f.: (4*x*(x-2) + x*(x-3)*cosh(x) + (x^2 -x +11)*sinh(x))/8. - G. C. Greubel, Jan 23 2020