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A137361 a(n) = Sum_{k=0..n/2} k*binomial(n-2*k, 3*k+2). 8
0, 0, 0, 0, 0, 0, 0, 1, 6, 21, 56, 126, 254, 480, 882, 1617, 2992, 5580, 10410, 19292, 35400, 64343, 116128, 208701, 374226, 670095, 1198164, 2138423, 3808148, 6766089, 11996042, 21229790, 37513896, 66202347, 116692472, 205458357, 361349662, 634845141, 1114205988 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: x^7/(x^5 + x^3 - 3*x^2 + 3*x - 1)^2. - Alois P. Heinz, Oct 23 2008

MAPLE

a:= n-> (Matrix(10, (i, j)-> if i=j-1 then 1 elif j=1 then [6, -15, 20, -15, 8, -7, 6, -2, 0, -1][i] else 0 fi)^n)[1, 8]:

seq(a(n), n=0..50);  # Alois P. Heinz, Oct 23 2008

MATHEMATICA

t[i_, j_] := If[i == j-1, 1, If[j == 1, {6, -15, 20, -15, 8, -7, 6, -2, 0, -1}[[i]] , 0]]; M = Array[t, {10, 10}]; a[n_] := MatrixPower[M, n][[1, 8]]; Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Feb 13 2015, after Alois P. Heinz *)

PROG

(MAGMA) [&+[k*Binomial(n-2*k, 3*k+2): k in [0..(n div 2)]]: n in [0..40]]; // Bruno Berselli, Feb 13 2015

CROSSREFS

Cf. A137356-A137360, A136444.

Sequence in context: A100356 A229886 A243740 * A058484 A145455 A145134

Adjacent sequences:  A137358 A137359 A137360 * A137362 A137363 A137364

KEYWORD

nonn

AUTHOR

Don Knuth, Apr 11 2008

STATUS

approved

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Last modified February 20 20:12 EST 2018. Contains 299385 sequences. (Running on oeis4.)