A003403 G.f.: (1 + x^3 + x^4 + ... + x^12 + x^15)/Product_{i=1..10} (1 - x^i).

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

Author

N. J. A. Sloane

Keywords

• nonn

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

• Ray Chandler, Table of n, a(n) for n = 0..1000
• 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).

Crossrefs

Cf. A003402, A003404, A003405, A029073, A256975, A256976, A256977.

Programs

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 *)

Extensions

Entry revised by N. J. A. Sloane, Apr 22 2015