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A134968 Number of convex functions from {1,...,n} to itself. 0
1, 1, 4, 16, 54, 168, 462, 1212, 2937, 6832, 15135, 32430, 66898, 134710, 263466, 504308, 944208, 1736575, 3134832, 5574947, 9760954, 16868418, 28771587, 48513127, 80867486, 133455462, 218041708, 353039664, 566580113, 901958971, 1424480451, 2233367056 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

That is, the number of sequences of length n, taking values in {1,...,n} that have nondecreasing first differences (nonnegative second differences).

LINKS

Table of n, a(n) for n=0..31.

FORMULA

See Mathematica code.

EXAMPLE

a(3)=16: the 16 sequences are 111, 112, 113, 123, 211, 212, 213, 222, 223, 311, 312, 313, 321, 322, 323 and 333.

MATHEMATICA

(*P[n, k]=number of ways to partition n into exactly k parts*) P[n_Integer, n_Integer] = 1; P[n_Integer, k_Integer] := P[n, k] = Sum[P[n - k, r], {r, 1, Min[n - k, k]}]

(*q[n, k]=number of ways to partition n into k-or-fewer parts*) q[0, 0] = 1; q[n_Integer, 0] = 0; q[n_Integer, k_Integer] := q[n, k] = q[n, k - 1] + P[n, k]

a[n_] := Sum[(n - Max[f, r])*P[r, s]*q[f, n - 1 - s], {r, 0, n - 1}, {s, 0, n - 1}, {f, 0, n - 1}]

CROSSREFS

Sequence in context: A121159 A239032 A254823 * A238419 A267227 A223944

Adjacent sequences:  A134965 A134966 A134967 * A134969 A134970 A134971

KEYWORD

nonn,nice

AUTHOR

Jacob A. Siehler, Feb 04 2008, Feb 06 2008

STATUS

approved

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)