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

3,2

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)

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)

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 *)

Prog

(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

Crossrefs

Sequence in context: A083364 A273499 A297520 * A004538 A146231 A186029

Adjacent sequences: A026391 A026392 A026393 * A026395 A026396 A026397

Keyword

nonn,easy

Author

Clark Kimberling

Status

approved