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A003403
G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).
(Formerly M1049)
4
1, 1, 2, 4, 7, 11, 18, 27, 41, 60, 87, 122, 172, 235, 320, 430, 572, 751, 982, 1268, 1629, 2074, 2625, 3297, 4123, 5118, 6324, 7771, 9506, 11567, 14023, 16917, 20335, 24343, 29039, 34510, 40885, 48265, 56811, 66661, 78001, 91001, 105901, 122902, 142291, 164329, 189347
OFFSET
0,3
COMMENTS
Enumerates certain triangular arrays of integers.
REFERENCES
J. C. P. Miller, On the enumeration of partially ordered sets of integers, pp. 109-124 of T. P. McDonough and V. C. Mavron, editors, Combinatorics: Proceedings of the Fourth British Combinatorial Conference 1973. London Mathematical Society, Lecture Note Series, Number 13, Cambridge University Press, NY, 1974. The g.f. is in Eq. (10.5).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 0, -2, -2, -3, 0, 2, 5, 4, 4, -2, -5, -6, -7, -2, 1, 7, 8, 7, 1, -2, -7, -6, -5, -2, 4, 4, 5, 2, 0, -3, -2, -2, 0, 1, 1, 1, -1).
MAPLE
(1+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^15)/mul(1-x^i, i=1..10);
MATHEMATICA
CoefficientList[Series[(1+Total[x^Range[3, 12] ]+x^15)/Product[1 - x^i, {i, 10}], {x, 0, 50}], x] (* Harvey P. Dale, Jun 24 2018 *)
KEYWORD
nonn
EXTENSIONS
Entry revised by N. J. A. Sloane, Apr 22 2015
STATUS
approved