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A089640 Enumeration of partial sums of 1+[1,2]+[2,3]+[1,2]+[2,3]+... 0
1, 1, 1, 1, 3, 4, 4, 6, 11, 15, 18, 27, 43, 59, 78, 115, 172, 239, 330, 480, 698, 980, 1379, 1988, 2856, 4037, 5726, 8211, 11737, 16656, 23700, 33885, 48341, 68749, 97941, 139811, 199316, 283780, 404442, 576879, 822223, 1171318, 1669543, 2380423 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..44.

FORMULA

a(n)=Sum{C(k, n-[(3n+2)/2]), k=0...n}, where C(n, k) is the usual binomial coefficient and [...] denotes the floor function. - John W. Layman, Jan 06 2004

EXAMPLE

a(6)=4 because we have 6=1+1+2+2=1+2+3=1+2+2+1=1+1+3+1.

PROG

(PARI) { n=15; v=vector(n); for (i=1, n, v[i]=vector(2^(i-1))); v[1][1]=1; for (i=2, n, k=length(v[i-1]); for (j=1, k, v[i][j]=v[i-1][j]+i%2+1; v[i][j+k]=v[i-1][j]+i%2+2)); c=vector(n); for (i=1, n, for (j=1, 2^(i-1), if (v[i][j]<=n, c[v[i][j]]++))); c }

CROSSREFS

Sequence in context: A047877 A280448 A100692 * A086659 A265887 A008473

Adjacent sequences:  A089637 A089638 A089639 * A089641 A089642 A089643

KEYWORD

nonn

AUTHOR

Jon Perry, Jan 01 2004

EXTENSIONS

Corrected and extended by John W. Layman, Jan 06 2004

STATUS

approved

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Last modified January 25 07:35 EST 2020. Contains 331241 sequences. (Running on oeis4.)