A278989 a(n) is the number of words of length n over an alphabet of size 4 that are in standard order and which have the property that every letter that appears in the word is repeated.

0, 0, 1, 1, 4, 11, 41, 162, 715, 3425, 16777, 80928, 379347, 1726375, 7654817, 33219630, 141692075, 596122477, 2480969257, 10237751324, 41963944275, 171103765747, 694775280993, 2812004330666, 11352134320523, 45736973060601, 183981143571721, 739167464021912, 2966826380664595, 11899055223201855

Offset

0,5

Links

Table of n, a(n) for n=0..29.

Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"

Formula

Conjectures from Colin Barker, Nov 25 2017: (Start)

G.f.: x^2*(1 - 19*x + 159*x^2 - 776*x^3 + 2474*x^4 - 5498*x^5 + 8993*x^6 - 11471*x^7 + 11815*x^8 - 9478*x^9 + 5348*x^10 - 1848*x^11 + 288*x^12) / ((1 - x)^4*(1 - 2*x)^3*(1 - 3*x)^2*(1 - 4*x)).

a(n) = 20*a(n-1) - 175*a(n-2) + 882*a(n-3) - 2835*a(n-4) + 6072*a(n-5) - 8777*a(n-6) + 8458*a(n-7) - 5204*a(n-8) + 1848*a(n-9) - 288*a(n-10) for n > 14.

(End)

Crossrefs

A row of the array in A278987.

Sequence in context: A278988 A214188 A214239 * A000296 A032265 A320155

Adjacent sequences: A278986 A278987 A278988 * A278990 A278991 A278992

Keyword

nonn

Author

N. J. A. Sloane, Dec 06 2016

Status

approved