A026394 a(n) = T(n,n-3), where T is the array in A026386.

1, 5, 17, 34, 75, 114, 202, 272, 425, 535, 771, 930, 1267, 1484, 1940, 2224, 2817, 3177, 3925, 4370, 5291, 5830, 6942, 7584, 8905, 9659, 11207, 12082, 13875, 14880, 16936, 18080, 20417, 21709, 24345, 25794, 28747, 30362, 33650, 35440, 39081, 41055, 45067

Offset: 3

Author

Clark Kimberling

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 3..1000
• Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1)

Programs

Mathematica

t[n_, 0] := 1; t[n_, n_] := 1; t[n_, k_] := t[n, k] = Which[EvenQ@ n, t[n - 1, k - 1] + t[n - 1, k], OddQ@ n, t[n - 1, k - 1] + t[n - 1, k] + t[n - 2, k - 1]]; Table[t[n, n - 3], {n, 3, 45}] (* Michael De Vlieger, Jan 29 2016, after Clark Kimberling at A026386 *)

PARI

Vec(x^3*(1+4*x+9*x^2+5*x^3+8*x^4)/((1-x)^4*(1+x)^3) + O(x^100)) \\ Colin Barker, Jan 29 2016

Formula

G.f.: x^3*(1+4*x+9*x^2+5*x^3+8*x^4) / ((1-x)^4*(1+x)^3). - Emeric Deutsch, Feb 18 2004

From Colin Barker, Jan 29 2016: (Start)

a(n) = (18*n^3-9*(-1)^n*n^2-111*n^2+53*(-1)^n*n+243*n-75*(-1)^n-181)/32.

a(n) = (9*n^3-60*n^2+148*n-128)/16 for n even.

a(n) = (9*n^3-51*n^2+95*n-53)/16 for n odd.

(End)