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A026394
a(n) = T(n,n-3), where T is the array in A026386.
1
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
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
KEYWORD
nonn,easy
STATUS
approved